If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## College Algebra

Unit 1: linear equations and inequalities, unit 2: graphs and forms of linear equations, unit 3: functions, unit 4: quadratics: multiplying and factoring, unit 5: quadratic functions and equations, unit 6: complex numbers, unit 7: exponents and radicals, unit 8: rational expressions and equations, unit 9: relating algebra and geometry, unit 10: polynomial arithmetic, unit 11: advanced function types, unit 12: transformations of functions, unit 13: rational exponents and radicals, unit 14: logarithms.

- For a new problem, you will need to begin a new live expert session.
- You can contact support with any questions regarding your current subscription.
- You will be able to enter math problems once our session is over.
- I am only able to help with one math problem per session. Which problem would you like to work on?
- Does that make sense?
- I am currently working on this problem.
- Are you still there?
- It appears we may have a connection issue. I will end the session - please reconnect if you still need assistance.
- Let me take a look...
- Can you please send an image of the problem you are seeing in your book or homework?
- If you click on "Tap to view steps..." you will see the steps are now numbered. Which step # do you have a question on?
- Please make sure you are in the correct subject. To change subjects, please exit out of this live expert session and select the appropriate subject from the menu located in the upper left corner of the Mathway screen.
- What are you trying to do with this input?
- While we cover a very wide range of problems, we are currently unable to assist with this specific problem. I spoke with my team and we will make note of this for future training. Is there a different problem you would like further assistance with?
- Mathway currently does not support this subject. We are more than happy to answer any math specific question you may have about this problem.
- Mathway currently does not support Ask an Expert Live in Chemistry. If this is what you were looking for, please contact support.
- Mathway currently only computes linear regressions.
- We are here to assist you with your math questions. You will need to get assistance from your school if you are having problems entering the answers into your online assignment.
- Phone support is available Monday-Friday, 9:00AM-10:00PM ET. You may speak with a member of our customer support team by calling 1-800-876-1799.
- Have a great day!
- Hope that helps!
- You're welcome!
- Per our terms of use, Mathway's live experts will not knowingly provide solutions to students while they are taking a test or quiz.

Please ensure that your password is at least 8 characters and contains each of the following:

- a special character: @$#!%*?&

- 4.2 Modeling with Linear Functions
- Introduction to Prerequisites
- 1.1 Real Numbers: Algebra Essentials
- 1.2 Exponents and Scientific Notation
- 1.3 Radicals and Rational Exponents
- 1.4 Polynomials
- 1.5 Factoring Polynomials
- 1.6 Rational Expressions
- Key Equations
- Key Concepts
- Review Exercises
- Practice Test
- Introduction to Equations and Inequalities
- 2.1 The Rectangular Coordinate Systems and Graphs
- 2.2 Linear Equations in One Variable
- 2.3 Models and Applications
- 2.4 Complex Numbers
- 2.5 Quadratic Equations
- 2.6 Other Types of Equations
- 2.7 Linear Inequalities and Absolute Value Inequalities
- Introduction to Functions
- 3.1 Functions and Function Notation
- 3.2 Domain and Range
- 3.3 Rates of Change and Behavior of Graphs
- 3.4 Composition of Functions
- 3.5 Transformation of Functions
- 3.6 Absolute Value Functions
- 3.7 Inverse Functions
- Introduction to Linear Functions
- 4.1 Linear Functions
- 4.3 Fitting Linear Models to Data
- Introduction to Polynomial and Rational Functions
- 5.1 Quadratic Functions
- 5.2 Power Functions and Polynomial Functions
- 5.3 Graphs of Polynomial Functions
- 5.4 Dividing Polynomials
- 5.5 Zeros of Polynomial Functions
- 5.6 Rational Functions
- 5.7 Inverses and Radical Functions
- 5.8 Modeling Using Variation
- Introduction to Exponential and Logarithmic Functions
- 6.1 Exponential Functions
- 6.2 Graphs of Exponential Functions
- 6.3 Logarithmic Functions
- 6.4 Graphs of Logarithmic Functions
- 6.5 Logarithmic Properties
- 6.6 Exponential and Logarithmic Equations
- 6.7 Exponential and Logarithmic Models
- 6.8 Fitting Exponential Models to Data
- Introduction to Systems of Equations and Inequalities
- 7.1 Systems of Linear Equations: Two Variables
- 7.2 Systems of Linear Equations: Three Variables
- 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
- 7.4 Partial Fractions
- 7.5 Matrices and Matrix Operations
- 7.6 Solving Systems with Gaussian Elimination
- 7.7 Solving Systems with Inverses
- 7.8 Solving Systems with Cramer's Rule
- Introduction to Analytic Geometry
- 8.1 The Ellipse
- 8.2 The Hyperbola
- 8.3 The Parabola
- 8.4 Rotation of Axes
- 8.5 Conic Sections in Polar Coordinates
- Introduction to Sequences, Probability and Counting Theory
- 9.1 Sequences and Their Notations
- 9.2 Arithmetic Sequences
- 9.3 Geometric Sequences
- 9.4 Series and Their Notations
- 9.5 Counting Principles
- 9.6 Binomial Theorem
- 9.7 Probability

## Learning Objectives

In this section, you will:

- Build linear models from verbal descriptions.
- Model a set of data with a linear function.

Elan is a college student who plans to spend a summer in Seattle. Elan has saved $3,500 for their trip and anticipates spending $400 each week on rent, food, and activities. How can we write a linear model to represent this situation? What would be the x -intercept, and what can Elan learn from it? To answer these and related questions, we can create a model using a linear function. Models such as this one can be extremely useful for analyzing relationships and making predictions based on those relationships. In this section, we will explore examples of linear function models.

## Building Linear Models from Verbal Descriptions

When building linear models to solve problems involving quantities with a constant rate of change, we typically follow the same problem strategies that we would use for any type of function. Let’s briefly review them:

- Identify changing quantities, and then define descriptive variables to represent those quantities. When appropriate, sketch a picture or define a coordinate system.
- Carefully read the problem to identify important information. Look for information that provides values for the variables or values for parts of the functional model, such as slope and initial value.
- Carefully read the problem to determine what we are trying to find, identify, solve, or interpret.
- Identify a solution pathway from the provided information to what we are trying to find. Often this will involve checking and tracking units, building a table, or even finding a formula for the function being used to model the problem.
- When needed, write a formula for the function.
- Solve or evaluate the function using the formula.
- Reflect on whether your answer is reasonable for the given situation and whether it makes sense mathematically.
- Clearly convey your result using appropriate units, and answer in full sentences when necessary.

Now let’s take a look at the student in Seattle. In Elan’s situation, there are two changing quantities: time and money. The amount of money they have remaining while on vacation depends on how long they stay. We can use this information to define our variables, including units.

So, the amount of money remaining depends on the number of weeks: M ( t ) M ( t ) .

Notice that the unit of dollars per week matches the unit of our output variable divided by our input variable. Also, because the slope is negative, the linear function is decreasing. This should make sense because she is spending money each week.

The rate of change is constant, so we can start with the linear model M ( t ) = m t + b . M ( t ) = m t + b . Then we can substitute the intercept and slope provided.

To find the t- intercept (horizontal axis intercept), we set the output to zero, and solve for the input.

The t -intercept (horizontal axis intercept) is 8.75 weeks. Because this represents the input value when the output will be zero, we could say that Elan will have no money left after 8.75 weeks.

When modeling any real-life scenario with functions, there is typically a limited domain over which that model will be valid—almost no trend continues indefinitely. Here the domain refers to the number of weeks. In this case, it doesn’t make sense to talk about input values less than zero. A negative input value could refer to a number of weeks before Elan saved $3,500, but the scenario discussed poses the question once they saved $3,500 because this is when the trip and subsequent spending starts. It is also likely that this model is not valid after the t -intercept (horizontal axis intercept), unless Elan uses a credit card and goes into debt. The domain represents the set of input values, so the reasonable domain for this function is 0 ≤ t ≤ 8.75. 0 ≤ t ≤ 8.75.

In this example, we were given a written description of the situation. We followed the steps of modeling a problem to analyze the information. However, the information provided may not always be the same. Sometimes we might be provided with an intercept. Other times we might be provided with an output value. We must be careful to analyze the information we are given, and use it appropriately to build a linear model.

## Using a Given Intercept to Build a Model

Some real-world problems provide the vertical axis intercept, which is the constant or initial value. Once the vertical axis intercept is known, the t -intercept (horizontal axis intercept) can be calculated. Suppose, for example, that Hannah plans to pay off a no-interest loan from her parents. Her loan balance is $1,000. She plans to pay $250 per month until her balance is $0. The y -intercept is the initial amount of her debt, or $1,000. The rate of change, or slope, is -$250 per month. We can then use the slope-intercept form and the given information to develop a linear model.

Now we can set the function equal to 0, and solve for x x to find the x -intercept.

The x -intercept is the number of months it takes her to reach a balance of $0. The x -intercept is 4 months, so it will take Hannah four months to pay off her loan.

## Using a Given Input and Output to Build a Model

Many real-world applications are not as direct as the ones we just considered. Instead they require us to identify some aspect of a linear function. We might sometimes instead be asked to evaluate the linear model at a given input or set the equation of the linear model equal to a specified output.

Given a word problem that includes two pairs of input and output values, use the linear function to solve a problem.

- Identify the input and output values.
- Convert the data to two coordinate pairs.
- Find the slope.
- Write the linear model.
- Use the model to make a prediction by evaluating the function at a given x -value.
- Use the model to identify an x -value that results in a given y -value.
- Answer the question posed.

## Using a Linear Model to Investigate a Town’s Population

A town’s population has been growing linearly. In 2004, the population was 6,200. By 2009, the population had grown to 8,100. Assume this trend continues.

- ⓐ Predict the population in 2013.
- ⓑ Identify the year in which the population will reach 15,000.

The two changing quantities are the population size and time. While we could use the actual year value as the input quantity, doing so tends to lead to very cumbersome equations because the y -intercept would correspond to the year 0, more than 2000 years ago!

To make computation a little nicer, we will define our input as the number of years since 2004.

To predict the population in 2013 ( t = 9 t = 9 ), we would first need an equation for the population. Likewise, to find when the population would reach 15,000, we would need to solve for the input that would provide an output of 15,000. To write an equation, we need the initial value and the rate of change, or slope.

To determine the rate of change, we will use the change in output per change in input.

The problem gives us two input-output pairs. Converting them to match our defined variables, the year 2004 would correspond to t = 0 , t = 0 , giving the point ( 0 , 6200 ) . ( 0 , 6200 ) . Notice that through our clever choice of variable definition, we have “given” ourselves the y -intercept of the function. The year 2009 would correspond to t = 5, t = 5, giving the point ( 5 , 8100 ) . ( 5 , 8100 ) .

The two coordinate pairs are ( 0 , 6200 ) ( 0 , 6200 ) and ( 5 , 8100 ) . ( 5 , 8100 ) . Recall that we encountered examples in which we were provided two points earlier in the chapter. We can use these values to calculate the slope.

We already know the y -intercept of the line, so we can immediately write the equation:

To predict the population in 2013, we evaluate our function at t = 9. t = 9.

If the trend continues, our model predicts a population of 9,620 in 2013.

To find when the population will reach 15,000, we can set P ( t ) = 15000 P ( t ) = 15000 and solve for t . t .

Our model predicts the population will reach 15,000 in a little more than 23 years after 2004, or somewhere around the year 2027.

A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25 to produce each doughnut.

ⓐ Write a linear model to represent the cost C C of the company as a function of x , x , the number of doughnuts produced. ⓑ Find and interpret the y -intercept.

A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was 36,800. Assume this trend continues.

- ⓐ Predict the population in 2014.
- ⓑ Identify the year in which the population will reach 54,000.

## Using a Diagram to Build a Model

It is useful for many real-world applications to draw a picture to gain a sense of how the variables representing the input and output may be used to answer a question. To draw the picture, first consider what the problem is asking for. Then, determine the input and the output. The diagram should relate the variables. Often, geometrical shapes or figures are drawn. Distances are often traced out. If a right triangle is sketched, the Pythagorean Theorem relates the sides. If a rectangle is sketched, labeling width and height is helpful.

## Using a Diagram to Model Distance Walked

Anna and Emanuel start at the same intersection. Anna walks east at 4 miles per hour while Emanuel walks south at 3 miles per hour. They are communicating with a two-way radio that has a range of 2 miles. How long after they start walking will they fall out of radio contact?

In essence, we can partially answer this question by saying they will fall out of radio contact when they are 2 miles apart, which leads us to ask a new question:

"How long will it take them to be 2 miles apart"?

In this problem, our changing quantities are time and position, but ultimately we need to know how long will it take for them to be 2 miles apart. We can see that time will be our input variable, so we’ll define our input and output variables.

Because it is not obvious how to define our output variable, we’ll start by drawing a picture such as Figure 2 .

Initial Value: They both start at the same intersection so when t = 0 , t = 0 , the distance traveled by each person should also be 0. Thus the initial value for each is 0.

Rate of Change: Anna is walking 4 miles per hour and Emanuel is walking 3 miles per hour, which are both rates of change. The slope for A A is 4 and the slope for E E is 3.

Using those values, we can write formulas for the distance each person has walked.

For this problem, the distances from the starting point are important. To notate these, we can define a coordinate system, identifying the “starting point” at the intersection where they both started. Then we can use the variable, A , A , which we introduced above, to represent Anna’s position, and define it to be a measurement from the starting point in the eastward direction. Likewise, can use the variable, E , E , to represent Emanuel’s position, measured from the starting point in the southward direction. Note that in defining the coordinate system, we specified both the starting point of the measurement and the direction of measure.

We can then define a third variable, D , D , to be the measurement of the distance between Anna and Emanuel. Showing the variables on the diagram is often helpful, as we can see from Figure 3 .

Recall that we need to know how long it takes for D , D , the distance between them, to equal 2 miles. Notice that for any given input t , t , the outputs A ( t ) , E ( t ) , A ( t ) , E ( t ) , and D ( t ) D ( t ) represent distances.

Figure 2 shows us that we can use the Pythagorean Theorem because we have drawn a right angle.

Using the Pythagorean Theorem, we get:

In this scenario we are considering only positive values of t , t , so our distance D ( t ) D ( t ) will always be positive. We can simplify this answer to D ( t ) = 5 t . D ( t ) = 5 t . This means that the distance between Anna and Emanuel is also a linear function. Because D D is a linear function, we can now answer the question of when the distance between them will reach 2 miles. We will set the output D ( t ) = 2 D ( t ) = 2 and solve for t . t .

They will fall out of radio contact in 0.4 hour, or 24 minutes.

Should I draw diagrams when given information based on a geometric shape?

Yes. Sketch the figure and label the quantities and unknowns on the sketch.

## Using a Diagram to Model Distance Between Cities

There is a straight road leading from the town of Westborough to Agritown 30 miles east and 10 miles north. Partway down this road, it junctions with a second road, perpendicular to the first, leading to the town of Eastborough. If the town of Eastborough is located 20 miles directly east of the town of Westborough, how far is the road junction from Westborough?

It might help here to draw a picture of the situation. See Figure 4 . It would then be helpful to introduce a coordinate system. While we could place the origin anywhere, placing it at Westborough seems convenient. This puts Agritown at coordinates ( 3 0 , 1 0 ) , ( 3 0 , 1 0 ) , and Eastborough at ( 2 0 , 0 ) . ( 2 0 , 0 ) .

Using this point along with the origin, we can find the slope of the line from Westborough to Agritown.

Now we can write an equation to describe the road from Westborough to Agritown.

From this, we can determine the perpendicular road to Eastborough will have slope m = – 3. m = – 3. Because the town of Eastborough is at the point (20, 0), we can find the equation.

We can now find the coordinates of the junction of the roads by finding the intersection of these lines. Setting them equal,

The roads intersect at the point (18, 6). Using the distance formula, we can now find the distance from Westborough to the junction.

One nice use of linear models is to take advantage of the fact that the graphs of these functions are lines. This means real-world applications discussing maps need linear functions to model the distances between reference points.

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison. If the town of Garrison is located 22 miles directly east of the town of Timpson, how far is the road junction from Timpson?

## Modeling a Set of Data with Linear Functions

Real-world situations including two or more linear functions may be modeled with a system of linear equations . Remember, when solving a system of linear equations, we are looking for points the two lines have in common. Typically, there are three types of answers possible, as shown in Figure 5 .

Given a situation that represents a system of linear equations, write the system of equations and identify the solution.

- Identify the input and output of each linear model.
- Identify the slope and y -intercept of each linear model.
- Find the solution by setting the two linear functions equal to another and solving for x , x , or find the point of intersection on a graph.

## Building a System of Linear Models to Choose a Truck Rental Company

Jamal is choosing between two truck-rental companies. The first, Keep on Trucking, Inc., charges an up-front fee of $20, then 59 cents a mile. The second, Move It Your Way, charges an up-front fee of $16, then 63 cents a mile 4 . When will Keep on Trucking, Inc. be the better choice for Jamal?

The two important quantities in this problem are the cost and the number of miles driven. Because we have two companies to consider, we will define two functions in Table 1 .

A linear function is of the form f ( x ) = m x + b . f ( x ) = m x + b . Using the rates of change and initial charges, we can write the equations

Using these equations, we can determine when Keep on Trucking, Inc., will be the better choice. Because all we have to make that decision from is the costs, we are looking for when Move It Your Way, will cost less, or when K ( d ) < M ( d ) . K ( d ) < M ( d ) . The solution pathway will lead us to find the equations for the two functions, find the intersection, and then see where the K ( d ) K ( d ) function is smaller.

These graphs are sketched in Figure 6 , with K ( d ) K ( d ) in blue.

To find the intersection, we set the equations equal and solve:

This tells us that the cost from the two companies will be the same if 100 miles are driven. Either by looking at the graph, or noting that K ( d ) K ( d ) is growing at a slower rate, we can conclude that Keep on Trucking, Inc. will be the cheaper price when more than 100 miles are driven, that is d > 100 d > 100 .

Access this online resource for additional instruction and practice with linear function models.

- Interpreting a Linear Function

## 4.2 Section Exercises

Explain how to find the input variable in a word problem that uses a linear function.

Explain how to find the output variable in a word problem that uses a linear function.

Explain how to interpret the initial value in a word problem that uses a linear function.

Explain how to determine the slope in a word problem that uses a linear function.

Find the area of a parallelogram bounded by the y -axis, the line x = 3 , x = 3 , the line f ( x ) = 1 + 2 x , f ( x ) = 1 + 2 x , and the line parallel to f ( x ) f ( x ) passing through ( 2 , 7 ) . ( 2 , 7 ) .

Find the area of a triangle bounded by the x -axis, the line f ( x ) = 12 – 1 3 x , f ( x ) = 12 – 1 3 x , and the line perpendicular to f ( x ) f ( x ) that passes through the origin.

Find the area of a triangle bounded by the y -axis, the line f ( x ) = 9 – 6 7 x , f ( x ) = 9 – 6 7 x , and the line perpendicular to f ( x ) f ( x ) that passes through the origin.

Find the area of a parallelogram bounded by the x -axis, the line g ( x ) = 2 , g ( x ) = 2 , the line f ( x ) = 3 x , f ( x ) = 3 x , and the line parallel to f ( x ) f ( x ) passing through ( 6 , 1 ) . ( 6 , 1 ) .

For the following exercises, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped to 4,700. Assume this trend continues.

Predict the population in 2016.

Identify the year in which the population will reach 0.

For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In 2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues.

Identify the year in which the population will reach 75,000.

For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years.

Find the linear function that models the town’s population P P as a function of the year, t , t , where t t is the number of years since the model began.

Find a reasonable domain and range for the function P . P .

If the function P P is graphed, find and interpret the x - and y -intercepts.

If the function P P is graphed, find and interpret the slope of the function.

When will the population reach 100,000?

What is the population in the year 12 years from the onset of the model?

For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

Find the linear function that models the baby’s weight W W as a function of the age of the baby, in months, t . t .

Find a reasonable domain and range for the function W . W .

If the function W W is graphed, find and interpret the x - and y -intercepts.

If the function W is graphed, find and interpret the slope of the function.

When did the baby weight 10.4 pounds?

What is the output when the input is 6.2?

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted.

Find the linear function that models the number of people inflicted with the common cold C C as a function of the year, t . t .

Find a reasonable domain and range for the function C . C .

If the function C C is graphed, find and interpret the x - and y -intercepts.

If the function C C is graphed, find and interpret the slope of the function.

When will the output reach 0?

In what year will the number of people be 9,700?

For the following exercises, use the graph in Figure 7 , which shows the profit, y , y , in thousands of dollars, of a company in a given year, t , t , where t t represents the number of years since 1980.

Find the linear function y , y , where y y depends on t , t , the number of years since 1980.

Find and interpret the y -intercept.

Find and interpret the x -intercept.

Find and interpret the slope.

For the following exercises, use the graph in Figure 8 , which shows the profit, y , y , in thousands of dollars, of a company in a given year, t , t , where t t represents the number of years since 1980.

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in Table 2 . Assume that the house values are changing linearly.

In which state have home values increased at a higher rate?

If these trends were to continue, what would be the median home value in Mississippi in 2010?

If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be (or were) equal in what year? (The answer might be absurd.)

For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Table 3 . Assume that the house values are changing linearly.

If these trends were to continue, what would be the median home value in Indiana in 2010?

## Real-World Applications

In 2004, a school population was 1001. By 2008 the population had grown to 1697. Assume the population is changing linearly.

- ⓐ How much did the population grow between the year 2004 and 2008?
- ⓑ How long did it take the population to grow from 1001 students to 1697 students?
- ⓒ What is the average population growth per year?
- ⓓ What was the population in the year 2000?
- ⓔ Find an equation for the population, P , P , of the school t years after 2000.
- ⓕ Using your equation, predict the population of the school in 2011.

In 2003, a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly.

- ⓐ How much did the population grow between the year 2003 and 2007?
- ⓑ How long did it take the population to grow from 1431 people to 2134 people?
- ⓔ Find an equation for the population, P , P , of the town t t years after 2000.
- ⓕ Using your equation, predict the population of the town in 2014.

A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used for voice or video calling. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.

- ⓐ Find a linear equation for the monthly cost of the cell plan as a function of x , the number of monthly minutes used.
- ⓑ Interpret the slope and y -intercept of the equation.
- ⓒ Use your equation to find the total monthly cost if 687 minutes are used.

A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 and then a certain amount of money per megabyte (MB) of data used on the phone. If a customer uses 20 MB, the monthly cost will be $11.20. If the customer uses 130 MB, the monthly cost will be $17.80.

- ⓐ Find a linear equation for the monthly cost of the data plan as a function of x , x , the number of MB used.
- ⓒ Use your equation to find the total monthly cost if 250 MB are used.

In 1991, the moose population in a park was measured to be 4,360. By 1999, the population was measured again to be 5,880. Assume the population continues to change linearly.

- ⓐ Find a formula for the moose population, P since 1990.
- ⓑ What does your model predict the moose population to be in 2003?

In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. Let the input be years since 2003.

- ⓐ Find a formula for the owl population, P . P . Let the input be years since 2003.
- ⓑ What does your model predict the owl population to be in 2012?

The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year.

- ⓐ Give a linear equation for the remaining federal helium reserves, R , R , in terms of t , t , the number of years since 2010.
- ⓑ In 2015, what will the helium reserves be?
- ⓒ If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?

Suppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year:

- ⓐ Give a linear equation for the remaining oil reserves, R , R , in terms of t , t , the number of years since now.
- ⓑ Seven years from now, what will the oil reserves be?
- ⓒ If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?

You are choosing between two different prepaid cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?

You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window. How many windows would you need to have for the second company to be preferable?

When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $17,000 a year with a commission of 12% of your sales

Option B: Base salary of $20,000 a year with a commission of 5% of your sales

How much jewelry would you need to sell for option A to produce a larger income?

When hired at a new job selling electronics, you are given two pay options:

Option A: Base salary of $14,000 a year with a commission of 10% of your sales

Option B: Base salary of $19,000 a year with a commission of 4% of your sales

How much electronics would you need to sell for option A to produce a larger income?

Option A: Base salary of $20,000 a year with a commission of 12% of your sales

Option B: Base salary of $26,000 a year with a commission of 3% of your sales

Option A: Base salary of $10,000 a year with a commission of 9% of your sales

Option B: Base salary of $20,000 a year with a commission of 4% of your sales

- 4 Rates retrieved Aug 2, 2010 from http://www.budgettruck.com and http://www.uhaul.com/

As an Amazon Associate we earn from qualifying purchases.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/college-algebra-2e/pages/1-introduction-to-prerequisites

- Authors: Jay Abramson
- Publisher/website: OpenStax
- Book title: College Algebra 2e
- Publication date: Dec 21, 2021
- Location: Houston, Texas
- Book URL: https://openstax.org/books/college-algebra-2e/pages/1-introduction-to-prerequisites
- Section URL: https://openstax.org/books/college-algebra-2e/pages/4-2-modeling-with-linear-functions

© Jun 22, 2023 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

- + ACCUPLACER Mathematics
- + ACT Mathematics
- + AFOQT Mathematics
- + ALEKS Tests
- + ASVAB Mathematics
- + ATI TEAS Math Tests
- + Common Core Math
- + DAT Math Tests
- + FSA Tests
- + FTCE Math
- + GED Mathematics
- + Georgia Milestones Assessment
- + GRE Quantitative Reasoning
- + HiSET Math Exam
- + HSPT Math
- + ISEE Mathematics
- + PARCC Tests
- + Praxis Math
- + PSAT Math Tests
- + PSSA Tests
- + SAT Math Tests
- + SBAC Tests
- + SIFT Math
- + SSAT Math Tests
- + STAAR Tests
- + TABE Tests
- + TASC Math
- + TSI Mathematics
- + ACT Math Worksheets
- + Accuplacer Math Worksheets
- + AFOQT Math Worksheets
- + ALEKS Math Worksheets
- + ASVAB Math Worksheets
- + ATI TEAS 6 Math Worksheets
- + FTCE General Math Worksheets
- + GED Math Worksheets
- + 3rd Grade Mathematics Worksheets
- + 4th Grade Mathematics Worksheets
- + 5th Grade Mathematics Worksheets
- + 6th Grade Math Worksheets
- + 7th Grade Mathematics Worksheets
- + 8th Grade Mathematics Worksheets
- + 9th Grade Math Worksheets
- + HiSET Math Worksheets
- + HSPT Math Worksheets
- + ISEE Middle-Level Math Worksheets
- + PERT Math Worksheets
- + Praxis Math Worksheets
- + PSAT Math Worksheets
- + SAT Math Worksheets
- + SIFT Math Worksheets
- + SSAT Middle Level Math Worksheets
- + 7th Grade STAAR Math Worksheets
- + 8th Grade STAAR Math Worksheets
- + THEA Math Worksheets
- + TABE Math Worksheets
- + TASC Math Worksheets
- + TSI Math Worksheets
- + AFOQT Math Course
- + ALEKS Math Course
- + ASVAB Math Course
- + ATI TEAS 6 Math Course
- + CHSPE Math Course
- + FTCE General Knowledge Course
- + GED Math Course
- + HiSET Math Course
- + HSPT Math Course
- + ISEE Upper Level Math Course
- + SHSAT Math Course
- + SSAT Upper-Level Math Course
- + PERT Math Course
- + Praxis Core Math Course
- + SIFT Math Course
- + 8th Grade STAAR Math Course
- + TABE Math Course
- + TASC Math Course
- + TSI Math Course
- + Number Properties Puzzles
- + Algebra Puzzles
- + Geometry Puzzles
- + Intelligent Math Puzzles
- + Ratio, Proportion & Percentages Puzzles
- + Other Math Puzzles

## CLEP College Algebra Worksheets: FREE & Printable

Looking for FREE printable CLEP College Algebra worksheets to help you review the math concepts? Here's a collection of PDF worksheets for all CLEP College Algebra topics.

Need great CLEP College Algebra worksheets to help your students prepare for the CLEP College Algebra test? If so, then you are in the right place.

Here is a comprehensive and perfect collection of FREE CLEP College Algebra worksheets that would help students in CLEP Algebra preparation and practice.

There is also a FREE CLEP College Algebra Practice Test

Hope you enjoy it!

IMPORTANT: COPYRIGHT TERMS: These worksheets are for personal use. Worksheets may not be uploaded to the internet, including classroom/personal websites or network drives. You can download the worksheets and print as many as you need. You can distribute the printed copies to your students, teachers, tutors, and friends.

You Do NOT have permission to send these worksheets to anyone in any way (via email, text messages, or other ways). They MUST download the worksheets themselves. You can send the address of this page to your students, tutors, friends, etc.

The Absolute Best Book to Ace the CLEP College Algebra Test

## CLEP College Algebra Prep 2020 A Comprehensive Review and Step-By-Step Guide to Preparing for the CLEP College Algebra Test

Fundamentals and building blocks.

- Adding and Subtracting Integers
- Multiplying and Dividing Integers
- Order of Operations
- Ordering Integers and Numbers
- Integers and Absolute Value
- Simplifying Ratios
- Proportional Ratios
- Similarity and Ratios
- Ratio and Rates Word Problems
- Percentage Calculations
- Percent Problems
- Discount, Tax and Tip
- Percent of Change
- Simple Interest

## Algebraic Expressions

- Simplifying Variable Expressions
- Simplifying Polynomial Expressions
- Translate Phrases into an Algebraic Statement
- The Distributive Property
- Evaluating One Variable Expressions
- Evaluating Two Variables Expressions
- Combining like Terms

## Equations and Inequalities

- One-Step Equations
- Multi-Step Equations
- Graphing Single–Variable Inequalities
- One-Step Inequalities
- Multi-Step Inequalities
- Systems of Equations
- Systems of Equations Word Problems
- Quadratic Equation

## Linear Functions

- Finding Slope
- Graphing Lines Using Line Equation
- Writing Linear Equations
- Graphing Linear Inequalities
- Finding Midpoint
- Finding Distance of Two Points

## Exponents and Radicals

- Multiplication Property of Exponents
- Zero and Negative Exponents
- Division Property of Exponents
- Powers of Products and Quotients
- Negative Exponents and Negative Bases
- Scientific Notation
- Square Roots

## Polynomials

- Writing Polynomials in Standard Form
- Simplifying Polynomials
- Adding and Subtracting Polynomials
- Multiplying Monomials
- Multiplying and Dividing Monomials
- Multiplying a Polynomial and a Monomial
- Multiplying Binomials
- Factoring Trinomials
- Operations with Polynomials
- Solving a Quadratic Equation
- Quadratic Formula and the Discriminant
- Graphing Quadratic Functions
- Solving Quadratic Inequalities

## Complex Numbers

- Adding and Subtracting Complex Numbers
- Multiplying and Dividing Complex Numbers
- Rationalizing Imaginary Denominators
- Function Notation
- Adding and Subtracting Functions
- Multiplying and Dividing Functions
- Composition of Functions

## Trigonometric Functions

- Trig Ratios of General Angles
- Angles and Angle Measure
- Evaluating Trigonometric Function
- Arc Length and Sector Area

## Sequences and Series

- Arithmetic Sequences
- Geometric Sequences
- Adding and Subtracting Matrices
- Matrix Multiplication
- Rewriting Logarithms
- Evalu ating Logarithms
- Properties of Logarithms

Looking for the best resources to help you or your students succeed on the CLEP College Algebra test?

The Best Books to Ace the CLEP College Algebra Test

## Prepare for the CLEP College Algebra Test in 7 Days A Quick Study Guide with Two Full-Length CLEP College Algebra Practice Tests

Ace the clep college algebra in 30 days the ultimate crash course to beat the clep college algebra test, 5 full-length clep college algebra practice tests the practice you need to ace the clep college algebra test, clep college algebra exercise book student workbook and two realistic clep college algebra tests.

by: Reza about 4 years ago (category: Blog , Free Math Worksheets )

Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.

## Related to This Article

More math articles.

- Accuplacer Testing Accommodations for Disabilities
- Area and Perimeter
- 10 Most Common 6th Grade MEAP Math Questions
- 5 Tips on How to Score Higher on SAT Math
- The Ultimate 7th Grade IAR Math Course (+FREE Worksheets)
- How to Divide Polynomials Using Long Division?
- How to Compare Fractions?
- Top 10 7th Grade SBAC Math Practice Questions
- Hands-On Learning: How to Represent Subtraction of Fractions with Unlike Denominators Using Everyday Objects
- Estimating Differences

## What people say about "CLEP College Algebra Worksheets: FREE & Printable - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

## Leave a Reply Cancel reply

You must be logged in to post a comment.

## CLEP College Algebra Prep 2020-2021 The Most Comprehensive Review and Ultimate Guide to the CLEP College Algebra Test

Comprehensive clep college algebra practice book 2020 – 2021 complete coverage of all clep college algebra concepts + 2 full-length practice tests, clep college algebra study guide 2020 – 2021 a comprehensive review and step-by-step guide to preparing for the clep college algebra, clep college algebra tutor everything you need to help achieve an excellent score.

- ATI TEAS 6 Math
- ISEE Upper Level Math
- SSAT Upper-Level Math
- Praxis Core Math
- 8th Grade STAAR Math

Limited time only!

Save Over 23 %

It was $21.99 now it is $16.99

## Login and use all of our services.

Effortless Math services are waiting for you. login faster!

## Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

- Math Worksheets
- Math Courses
- Math Topics
- Math Puzzles
- Math eBooks
- GED Math Books
- HiSET Math Books
- ACT Math Books
- ISEE Math Books
- ACCUPLACER Books
- Premium Membership
- Youtube Videos
- Google Play
- Apple Store

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

- Bulk Orders
- Refund Policy

## Free Mathematics Tutorials

## Maths Practice For Algebra, College Algebra and Trigonometry

Practice questions, with answers, related to the maths Compass tests. The questions have hints to help students solve questions independently of the teacher. You may use the questions on these online worksheets to prepare for compass maths tests. The pages below can be viewed on Chrome.

- Algebra Practice Questions - Part 1
- Algebra Practice Questions - Part 2
- Algebra Practice Questions - Part 3
- Algebra Practice Questions - Part 4
- Evaluate Algebraic Expressions

## College Algebra

- College Algebra Practice Questions - Part 1
- College Algebra Practice Questions - Part 2

## Trigonometry

- Trigonometry Practice Questions - Part 1
- Trigonometry Practice Questions - Part 2

## Maths Applets

- Maths Applets to Understand Concepts

## Popular Pages

- Free Compass, SAT and ACT Math Placement Tests Practice

## Stay In Touch

- Privacy Policy

## Best 30 Algebra Books That Experts Highly Recommend

Learning algebra can be difficult and confusing, but it is an important skill to learn. Indeed, it is a great life skill that can help you in the future. However, learning algebra can be a lot easier if you have a good algebra book. Moreover, Algebra books often have algebra examples, step-by-step instructions, and many different problems for you to solve.

Well, choosing the right book for Algebra can be a difficult decision. Although, there are many different options available. In particular, we have put together a guide of the best books on algebra by skill level and test to guide you in this decision.

On the other hand, if you are looking for an algebra homework helper, don’t worry you can get the best algebra homework help from our experts. So, what are you waiting for get the best help now!

## Importance Of Algebra In Today’s World

Table of Contents

Algebra is a very important part of mathematics and is used in the sciences and the world of practical applications of linear algebra . However, it’s easy to see the importance of algebra in school, and learning the basics of math early in life will help a student throughout their education.

Besides, the implications of algebra in the outside world are vast. Further, the use of algebra in many fields such as accounting, engineering, science, and medicine.

## Do You Actually Need to Learn About Algebra Concepts?

This is a basic question that always raises in the average student’s mind. But yes, it is true that algebra makes your life’s calculations quite simpler. How? Let’s find out!

So, how does algebra come into play in everyday life? Assume you are requested to purchase eggs to decorate for Easter. You have 5 bucks and rush to the supermarket, where you discover that a carton of a dozen eggs costs $1.30. You can calculate how many eggs you can buy through a variety of methods, but because you’ve studied mathematics, your mind can answer this issue quickly.

To arrive at an answer, mentally divide the entire dollar amount by the cost of eggs. Here, algebra tells you that you can’t go beyond $5 utilizing the notion of inequalities.

Because you know you can only buy 3 cartons of eggs, you’ll walk up to the cashier with the correct number of cartons of eggs and won’t have to worry about overpaying. This is a simple example.

Another application of algebra in real life is with functions. Functions represent information linkages, similar to cause and effect. Although you may not believe you utilize functions at all, I can assure you that you do them virtually every day.

For example, you may be aware that when you microwave a glass of water, the longer you heat it, the hotter the water becomes. You know that the temperature of the water is a function of the time it is microwaved because of your understanding of functions.

Numerous real-life situations may be represented using functions and other algebraic ideas. Learning algebraic concepts helped to clarify your thinking by improving your understanding of these real-world situations and your ability to draw linkages between the facts.

## How can Algebra books help?

There are many ways that algebra books can help people who need to work on their algebra. For example, these books are a great way to introduce yourself to new topics that you may not have learned in class. There are also lots of practice problems and exercises in these books, which you find helpful in reaching my goals with algebra.

Furthermore, Algebra textbooks are a great way to improve how well you understand the subject and can make learning easier.

## Modes Of Availability of Algebra Books

There are two ways to availability of the best algebra books. Firstly, you can access these books through an online platform; Secondly, you can access books through an offline one.

## Online Mode

Here are the best textbooks that are available in algebra books online mode.

## 1. Regents Algebra I Power Pack Revised Edition

Writer: Gary M. Rubinstein M.S

Rating: ☆☆☆☆☆ (5 out of 5)

Online source: Kindle Unlimited, Scribd

Regents Algebra I Power Pack Revised Edition is an excellent book for a student who is interested in learning algebra. This book will cover finding x as well as polynomial functions and equations, linear equations, and quadratic equations.

Further, this book is extremely well organized, covering topics in perfect order. Besides, this book is full of exercises to help you understand and review the material.

## 2. Algebra Essentials Practice Workbook with Answers

Writer: Chris McMullen

Indeed, Algebra Essentials Practice Workbook with Answers is one of the best algebra books online. However, it is designed to help students with understanding the basic concepts of algebra and further their knowledge of the subject.

Moreover, it can help students if they are learning on their own or if they are taking a course in algebra.

## 3. Pre-Algebra: Order of Operations

Writer: Humble Math

Pre-Algebra: Order of Operations is also a helpful book to read if you’re having trouble solving problems with the order of operations. Moreover, this book is a vital concept to learn in math. It teaches the order in which mathematical operations should be solved.

In addition, the author is very easy to read and presents everything in a very logical order.

## Offline Mode

Here are some of the top best author’s books on Algebra which are not available in online mode. You can also read these books offline.

## 1. Richard W. Fisher

Book: No-Nonsense Algebra

Richard W. Fisher has written many books on algebra, but No-Nonsense Algebra is the best book. In addition, these books are helpful for students who are preparing for their high school algebra exams.

Indeed, Rick Fisher was a math instructor for the Oak Grove School District in San Jose, California, for over 31 years. Since graduating from San Jose State University in 1971 with a B.A. in mathematics, Rick has devoted his time to both teaching and developing unique award-winning math materials.

Buy & read this book:

This book is available in many libraries as well as on Amazon. You can also read it sitting at home by ordering it from Amazon.

## 2. Gilbert Strang

Book: Introduction to Linear Algebra

Indeed, Gilbert Strang is a professor of mathematics at the Massachusetts Institute of Technology, where his research focuses on analysis, linear algebra and PDEs.

Indeed, Gilbert Strang is an excellent writer for algebra. He also wrote about linear algebra, multivariable calculus, and calculus solutions.

The Linear Algebra book by L. LeBlanc is available at most bookstores across the world. Furthermore, you can also buy this book online at sites like amazon.com, which has a rather good price.

## 3. Lynette Long

Book: Painless Algebra

Lynette Long is a licensed psychologist and former college professor. Indeed, she has published more than twenty-five books and dozens of articles and has written two award-winning plays. A math education expert, she is particularly interested in the math achievement of young girls.

The Painless Algebra book is available at most bookstores as well as libraries. Moreover, you can also buy this book at amazon.com.

## Best Algebra Books for Beginners and High School

Here are some of the best algebra books for beginners and high school:

## Check Top Algebra Textbooks For Beginners

1. introduction to abstract algebra.

Writer: Benjamin Fine, Anthony M. Gaglione, Gerhard Rosenberger

Introduction to Abstract Algebra is the best book for algebra.

This is a tremendously good book, presented in larger type, which makes it extremely pleasant to read. Additionally, this book helps beginners fully understand groups, rings, semigroups, and monoids by rigorously building concepts from the first principles.

About the Author:

In fact, Benjamin Fine is a professor of mathematics at Fairfield University.

Indeed, Anthony M. Gaglione is a professor of mathematics at the United States Naval Academy.

Gerhard Rosenberger is a professor of mathematics at the University of Hamburg.

## 2. Abstract Algebra: An Interactive Approach

Author: William Paulsen

Abstract Algebra: An Interactive Approach is a book for algebra.

However, the textbook gives an introduction to algebra . Furthermore, this book teaches how students can better grasp difficult algebraic concepts through the use of computer programs.

In addition, this book encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.

Indeed, it is also an excellent book of algebra for beginners if you are just starting out.

In fact, William Paulsen, PhD, professor of mathematics, Arkansas State University, USA

## 3. An Introduction to Essential Algebraic Structures

Author: Martyn R. Dixon, PhD, Leonid A. Kurdachenko, Igor Ya. Subbotin

Rating: ☆☆☆☆ (4 out of 5)

An Introduction to Essential Algebraic Structures teaches an integrated approach to basic concepts of modern algebra. This book also highlights topics that play a major role in various branches of mathematics.

Further, this book begins with a discussion of set theory’s fundamental concepts before moving on to abstract algebra’s core notions and branches. Overall, this textbook is the best book for algebra.

Firstly, Martyn R. Dixon, PhD, is a Professor in the Department of Mathematics at the University of Alabama.

Secondly, Leonid A. Kurdachenko, PhD, is a Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine.

Thirdly, Igor Ya. Subbotin, PhD, is a Professor in the Department of Natural Sciences and Mathematics at the National University in Los Angeles, California.

Furthermore, there are some other books which are very useful for beginners.

## 4. Abstract Algebra

Author: Paul B. Garrett

## 5. Pure Mathematics for Beginners

Author: Steve Warner

## 6. Introduction to Relation Algebras

## 7. A History of Abstract Algebra

Author: Jeremy Gray

## Check Top Algebra Books For High School

Here are the top books about algebra for high school.

## 1. High School Algebra I Unlocked

Author: Princeton Review

High School Algebra I Unlocked focuses on giving you a wide range of key techniques to help you tackle subjects like Algebra.

However, you’ll discover the link between abstract concepts and their real-world applications and build confidence as your skills improve with this book.

Additionally, you’ll get plenty of practice, from fully guided examples to independent end-of-chapter drills and test-like samples.

The experts at The Princeton Review have been helping students, parents, and educators achieve the best results at every stage of the education process since 1981.

## 2. Algebra I Workbook For Dummies

Author: Mary Jane Sterling

This book is the solution to the Algebra brain block. In addition, with hundreds of practice and example problems mapped to the typical high school Algebra class, this book teaches how to crack the code in no time!

However, this book is the best way to learn algebra is to work on the problems and let the numbers fly.

About the author:

Indeed, Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra I For Dummies and Algebra II For Dummies.

## 3. McGraw-Hill Education Algebra I Review and Workbook

Author: Sandra Luna McCune

McGraw-Hill Education Algebra I Review and Workbook is one of the best books on algebra.

However, this book is very concise. Besides, this book is great for high-school students.

Furthermore, this book introduces concepts well and is fairly comprehensive. With this book, you will also learn how to apply Algebra I to practical situations.

About the author:

Indeed, Sandra Luna McCune, PhD, is a former Regents Professor who taught as a mathematics specialist at Stephen F. Austin State University.

Moreover, there are some other algebra books for high school that are very useful.

## 4. Practice Makes Perfect Algebra I Review and Workbook

Author: Carolyn Wheater

## 5. 101 Involved Algebra Problems with Answers

Author: Chris McMullen

## 6. Must Know High School Algebra

Author: Chris Monahan

## 7. Algebra II: Essential Practice for Advanced Math Topics

Author: Inc. Carson-Dellosa Publishing

## Top 10 college algebra books

1. College Algebra

Author: James Stewart, Lothar Redlin, Saleem Watson

2. Essentials of College Algebra

Author: Margaret Lial, John Hornsby, David Schneider

3. College Algebra with Intermediate Algebra: A Blended Course

Author: Judith Beecher, Judith Penna, Barbara Johnson

4. College Algebra DeMYSTiFieD

Author: Rhonda Huettenmueller

5. Algebra for College Students

Author: Jerome E. Kaufmann, Karen L. Schwitters

6. College Algebra with Modeling & Visualization

Author: Gary Rockswold

7. College Algebra: Real Mathematics, Real People

Author: Ron Larson

8. College Algebra, Books a la Carte Edition

Author: J.S. Ratti, Marcus McWaters, Leslaw Skrzypek

9. Algebra and Trigonometry with Analytic Geometry

Author: Earl W. Swokowski, Jeffery A. Cole

10. Functions and Change: A Modeling Approach to College Algebra

Author: Bruce Crauder, Benny Evans, Alan Noell

Thus, these are some college algebra books.

We hope you enjoyed our blog about algebra books. Moreover, we know that you can make the most of your algebraic lessons and complete all your homework with ease with this knowledge.

These are very good algebra books that provide not only clear examples but also easy to understand examples. Furthermore, algebra is one of the foundations for math, and it will help students to be prepared for more advanced math courses. Although, a well-formed best algebra textbook will offer you immeasurable support to enhance your expertise in all the topics of algebra.

## Frequently Asked Questions

Q1. what are the 4 types of algebra.

There are not four distinct algebra types, but different branches of algebra focus on different types of mathematical structures and techniques. Here are some examples:

1. Elementary algebra: This branch of algebra deals with manipulating and solving algebraic expressions, equations, and inequalities.

2. Abstract algebra: This branch of algebra focuses on the study of algebraic structures such as groups, rings, and fields.

3. Linear algebra: This branch of algebra studies vectors, matrices, and linear transformations.

4. Boolean algebra: This branch of algebra studies Boolean functions, which take binary inputs (0 or 1) and produce binary outputs.

## Q2.Why is it important to study algebra?

The ability to absorb complicated, evolving as well as abstract concepts stimulate the brain, allowing students to discover new ways of thinking. Algebra also help students in organizing their thoughts, making it easier for them to come up with appropriate responses in complex or dynamic situations.

## Related Posts

## Top 10 Economics Books For Beginners To Boost Your Skills

## Top 15 Best Books For Finance To Become A Billionaire

## Mathematics

Homework help & tutoring.

Our name 24HourAnswers means you can submit work 24 hours a day - it doesn't mean we can help you master what you need to know in 24 hours. If you make arrangements in advance, and if you are a very fast learner, then yes, we may be able to help you achieve your goals in 24 hours. Remember, high quality, customized help that's tailored around the needs of each individual student takes time to achieve. You deserve nothing less than the best, so give us the time we need to give you the best.

If you need assistance with old exams in order to prepare for an upcoming test, we can definitely help. We can't work with you on current exams, quizzes, or tests unless you tell us in writing that you have permission to do so. This is not usually the case, however.

We do not have monthly fees or minimum payments, and there are no hidden costs. Instead, the price is unique for every work order you submit. For tutoring and homework help, the price depends on many factors that include the length of the session, level of work difficulty, level of expertise of the tutor, and amount of time available before the deadline. You will be given a price up front and there is no obligation for you to pay. Homework library items have individual set prices.

We accept credit cards, debit cards, PayPal, Venmo, ApplePay, and GooglePay.

Mathematics is a broad subject, covering everything from the exploration of the universe to the study of subatomic particles. As part of your degree plan, your university or college most likely requires you to take at least one math course. Whether you're enrolled in advanced mathematics or general coursework, you may need to find a college math tutor online to ensure that you fully understand every lesson.

Because you have to use your knowledge from one math class in the next, developing a functional understanding of each concept and getting professional math help online is an essential part of your success. Some mathematics classes you may take throughout college include:

- General math
- Number theory

To ensure you thoroughly comprehend each topic, you'll need to use a trustworthy source any time you search for online help with math homework or assignments to ensure you solve your problems correctly and feel confident in your answers.

## Find a College Math Tutor Online

If you turn to online resources for extra help in math, you'll need more than an online math homework helper you can consult before class. To gain a comprehensive knowledge of every topic and apply it to future quizzes and exams, you should seek a reliable and trustworthy college math tutor online.

In addition to helping you succeed in your current and future math courses, the experienced and credentialed math tutors at 24HourAnswers can also help you improve your in-class performance and boost your overall GPA. Our services are tailored to your needs, so you'll receive the individualized help you need to succeed in your classes.

## Choose 24HourAnswers for Math Homework Help Online

When you use our live math help resources online, you'll experience enhanced learning taught by highly credentialed professionals. Most of our instructors have advanced degrees in their fields, and they're dedicated to going above and beyond to assist you with any issues you're experiencing. They can provide step-by-step solutions for your math homework or assignments with explanations to ensure that you understand every lesson thoroughly.

From number theory and advanced statistics to basic geometry and algebra , our math tutors can walk you through any problems you've encountered in a wide range of math courses. You can use our live math help online to:

- Prepare for an upcoming exam.
- Answer specific math homework questions.
- Develop a greater conceptual knowledge of different topics.
- Review in-class lessons or textbook chapters.
- Break down problems into digestible steps.

We are also available at any hour, so our professional tutors can help you with your math homework or assignment online day or night.

## Get Live Math Help Online Today

If you're enrolled in a mathematics course and don't feel confident in your knowledge of the material, we can help. At 24HourAnswers, we're committed to helping college students with math homework and assignments so they can reach their full potential, starting in the classroom. We can help you improve your overall performance or achieve a goal you've set for yourself in your mathematics course.

Our math tutors are adaptable and highly knowledgeable about an extensive range of mathematics topics, meaning they'll provide instruction on a personalized level to ensure you get the most out of your individual sessions. They can walk you through different problems, help you with your math homework or provide context for mathematics concepts.

To get started and improve your grades or overall class performance, reach out to us today . Our tutors can help you with your math homework or answer any questions you might have.

## To fulfill our tutoring mission of online education, our college math homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of mathematics. Our math tutors can help with all your assignments and projects, large or small, and we challenge you to find better online math tutoring anywhere.

College mathematics homework help.

Since we have tutors in all Mathematics related topics, we can provide a range of different services. Our online Mathematics tutors will:

- Provide specific insight for homework assignments.
- Review broad conceptual ideas and chapters.
- Simplify complex topics into digestible pieces of information.
- Answer any Mathematics related questions.
- Tailor instruction to fit your style of learning.

With these capabilities, our college Mathematics tutors will give you the tools you need to gain a comprehensive knowledge of Mathematics you can use in future courses.

## 24HourAnswers Online Mathematics Tutors

Our tutors are just as dedicated to your success in class as you are, so they are available around the clock to assist you with questions, homework, exam preparation and any Mathematics related assignments you need extra help completing.

In addition to gaining access to highly qualified tutors, you'll also strengthen your confidence level in the classroom when you work with us. This newfound confidence will allow you to apply your Mathematics knowledge in future courses and keep your education progressing smoothly.

Because our college Mathematics tutors are fully remote, seeking their help is easy. Rather than spend valuable time trying to find a local Mathematics tutor you can trust, just call on our tutors whenever you need them without any conflicting schedules getting in the way.

## IMAGES

## VIDEO

## COMMENTS

Quiz Unit test Course challenge Test your knowledge of the skills in this course. Start Course challenge Unit 1: Linear equations and inequalities 0/900 Mastery points Solving equations with one unknown Solutions to linear equations Multi-step linear inequalities

Chapter 1 Highlights Try It 1.1 Real Numbers: Algebra Essentials 1. ⓐ 11 1 ⓑ 3 1 ⓒ − 4 1 2. ⓐ 4 (or 4.0), terminating; ⓑ 0. 615384 ¯ , repeating; ⓒ -0.85, terminating 3. ⓐ rational and repeating; ⓑ rational and terminating; ⓒ irrational; ⓓ rational and terminating; ⓔ irrational 4. ⓐ positive, irrational; right ⓑ negative, rational; left

1. −13 2. 2 For the following exercises, evaluate the expression. 3. 2 ( x + 3) − 12; x = 2 4. y ( 3 + 3) 2 − 26; y = 1 5. Write the number in standard notation: 3.1415 × 10 6 6. Write the number in scientific notation: 0.0000000212. For the following exercises, simplify the expression. 7. −2 ⋅ ( 2 + 3 ⋅ 2 ) 2 + 144 8. 4 ( x + 3 ) − ( 6 x + 2 ) 9.

Section R-1: The Real-Number System Section R-2: Integer Exponents, Scientific Notation, and Order of Operations Section R-3: Addition, Subtraction, and Multiplication of Polynomials Section R-4: Factoring Section R-5: The Basics of Equation Solving Section R-6: Rational Expressions Section R-7: Radical Notation and Rational Exponents Page 54:

Verified Chapter P: Prerequisites: Fundamental Concepts of Algebra I Section P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Section P.2: Exponents and Scientific Notation Section P.3: Radicals and Rational Exponents Section P.4: Polynomials Section P.5: Factoring Polynomials Section P.6: Rational Expressions Page 90: Exercises

Chapter 1: Equations and Inequalities Section 1.1: Linear Equations Section 1.2: Applications and Modeling with Linear Equations Section 1.3: Complex Numbers Section 1.4: Quadratic Equations Section 1.5: Applications and Modeling with Quadratic Equations Section 1.6: Other Types of Equations and Applications Section 1.7: Inequalities Section 1.8:

5.2 Power Functions and Polynomial Functions. 1. f ( x) is a power function because it can be written as f ( x) = 8 x 5 . The other functions are not power functions. 2. As x approaches positive or negative infinity, f ( x ) decreases without bound: as x → ± ∞, f ( x) → − ∞ because of the negative coefficient. 3.

The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.

Now, with expert-verified solutions from College Algebra 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for College Algebra includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can ...

MyMathLab with Integrated Review is a new course option that includes additional review resources (skill check quizzes, personalized homework, review worksheets, and videos) at the beginning of each chapter in the College Algebra course. NEW! 25 Just-In-Time review topics are assignable in MyMathLab. NEW!

For courses in College Algebra. ... Personalize learning with MyLab Math. MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study ...

Book Details. Learn to think mathematically and develop genuine problem-solving skills with COLLEGE ALGEBRA, Seventh Edition. This straightforward and easy-to-use book will help you learn the fundamentals of algebra in a variety of practical ways. The book features new tools to help you succeed, such as learning objectives before each section ...

Free math problem solver answers your algebra homework questions with step-by-step explanations.

Basic Algebra 0.1 The Laws of Algebra Terminology and Notation. In this section we review the notations used in algebra. Some are peculiar to this book. For example the notation A:= B indicates that the equality holds by de nition of the notations involved. Two other notations which will become important when we solve equations are =) and ().

The rate of change, or slope, is -$250 per month. We can then use the slope-intercept form and the given information to develop a linear model. f ( x) = m x + b = −250 x + 1000. Now we can set the function equal to 0, and solve for x to find the x -intercept. 0 = −250 x + 1000 1000 = 250 x 4 = x x = 4.

College Algebra Problems with Answers. sample 1: Quadratic Functions . sample 2: Composite and Inverse Functions . sample 3: Exponential and Logarithmic Functions . sample 4: Graphs of Functions . sample 5: Find Domain and Range of Functions .

Comprehensive CLEP College Algebra Practice Book 2020 - 2021 Complete Coverage of all CLEP College Algebra Concepts + 2 Full-Length Practice Tests $ 19.99 $ 14 .99 Download

Become famous by teaching math. Our 2629 algebra tutors solved 748600 problems submitted by 336188 registered students, wrote 2365 lessons , 304 solvers , to be seen by thousands ! They become famous and promote their math sites. Click here to learn about algebra tutoring and how to promote your math website or a book .

Maths Practice For Algebra, College Algebra and Trigonometry. Practice questions, with answers, related to the maths Compass tests. The questions have hints to help students solve questions independently of the teacher. You may use the questions on these online worksheets to prepare for compass maths tests. The pages below can be viewed on Chrome.

Indeed, Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra I For Dummies and Algebra II For Dummies. 3. McGraw-Hill Education Algebra I Review and Workbook.

To fulfill our tutoring mission of online education, our college math homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of mathematics. Our math tutors can help with all your assignments and projects, large or small, and we challenge you to find better online ...

1. Solution - 8 Answered Questions from Homework 7.3. College Algebra lNone. Exponential Equations Different Bases. College Algebra lNone. Discover more from: College Algebra lMath 2386. University of La Verne. 85Documents.

Section P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Section P.2: Basic Rules of Algebra Section P.3: Exponents and Scientific Notation Section P.4: Radicals and Rational Exponents Section P.5: Polynomials Page 74: Mid-Chapter Check Point Section P.6: Factoring Polynomials Section P.7: Rational Expressions Page 101:

Now, with expert-verified solutions from College Algebra 5th Edition, you'll learn how to solve your toughest homework problems. Our resource for College Algebra includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can ...