2. Equations and Inequalities

Use Linear Equations to Solve Problems

Models and Applications

Finding a Mathematical Expression to Model a Situation - Basic Example

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

You invested $30,000 in two accounts paying 2.19% and 2.45% annual interest. If the total interest earned for the year was $705.88, how much was invested at each rate?

Solve word problems by solving equations with one variable

The length of a rectangular pool is 6 meters less than twice the width. If the pool’s perimeter is 126 meters, what are its dimensions?

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

A = 2lw + 2lh + 2wh for h

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court’s perimeter is 228 feet, what are the court’s dimensions?

In Exercises 36–43, use the five-step strategy for solving word problems. The length of a rectangular field is 6 yards less than triple the width. If the perimeter of the field is 340 yards, what are its dimensions?

After a 20% reduction, you purchase a television for $336. What was the television’s price before the reduction?

Solve equations with non-numerical coefficients

For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

A = (1/2)bh for b

Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement - Ex 1

Translating Between Math and Words

Solving A Literal Equation For One Variable

In Exercises 36–43, use the five-step strategy for solving word problems. An apartment complex has offered you a move-in special of 30% off the first month’s rent. If you pay $945 for the first month, what should you expect to pay for the second month when you must pay full price?

Exercises 141–143 will help you prepare for the material covered in the next section.

If the width of a rectangle is represented by x and the length is represented by x + 200, write a simplified algebraic expression that models the rectangle’s perimeter.

A job pays an annual salary of $57,900, which includes a holiday bonus of $1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?

Translating Problems Into Equations (Level 1 of 2)

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

1/R = 1/R1 + 1/R2 for R1

Exercises 19–20 involve markup, the amount added to the dealer’s cost of an item to arrive at the selling price of that item.

The selling price of a refrigerator is $1198. If the markup is 25% of the dealer’s cost, what is the dealer’s cost of the refrigerator?

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

Including a 17.4% hotel tax, your room in Chicago cost $287.63 per night. Find the nightly cost before the tax was added.

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

E = mc^2 for m

You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

S = P + Prt for r

A repair bill on a sailboat came to $2356, including $826 for parts and the remainder for labor. If the cost of labor is $90 per hour, how many hours of labor did it take to repair the sailboat?

Solving an Equation for a Specified Variable

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement - Ex 3

You are choosing between two gyms. One gym offers membership for a fee of $40 plus a monthly fee of $25. The other offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

An automobile repair shop charged a customer $1182, listing $357 for parts and the remainder for labor. If the cost of labor is $75 per hour, how many hours of labor did it take to repair the car?

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

V = (1/3)Bh for B

How to Solve for a Variable

How to Solve in Terms of a Variable

An electronic pass for a toll road costs $30. The toll is normally $5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe?

D = RT for R

Translating Problems Into Equations (Level 2 of 2)

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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1. Fundamental Concepts of Algebra

3. Functions and Graphs

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6. Systems of Equations and Inequalities

7. Matrices and Determinants

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9. Sequences, Induction, and Probability

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Solve Quadratic Equations by Factoring

Solve Quadratic Equations by the Square Root Property

Solve Quadratic Equations by Completing the Square

Solve Quadratic Equations Using the Quadratic Formula

Use the Discriminant to Determine the Number and Type of Solutions

Determine the Most Efficient Method to Use When Solving a Quadratic Equation

Solve Problems Modeled by Quadratic Equations

Quadratic Equations

Add and Subtract Complex Numbers

Multiply Complex Numbers

Divide Complex Numbers

Simplify square roots of negative numbers.

Perform Operations with Square Roots of Negative Numbers

Simplify powers of i

Complex Numbers

Solving Linear Equations in One Variable

Solving a Linear Equation Involving Fractions

Solve Rational Equations with Variables in the Denominators

Recognize Identities, Conditional Equations, Inconsistent Equations

Solve Applied Problems Using Mathematical Models

Linear Equations and Rational Equations

Use Interval Notation

Find Intersections and Unions of Intervals

Solve Linear Inequalities

Rationalize Inequalities with No Solution 

Solve Compound Inequalities

Solve Absolute Value Inequalities

Linear Inequalities and Absolute Value Inequalities

Plotting Points in the Rectangular Coordinate System

Graphing an Equation Using the Point-Plotting Method

Understanding the Viewing Rectangle

Identifying Intercepts

Interpret Information Given by Graphs

Graphs and Graphing Utilities

Solving Polynomial Equations by Factoring

Solve Radical Equations

Solve Equations with Rational Exponents

Solve Equations That Are Quadratic In Form

Solving Equations Involving Absolute Value

Solve Problems Modeled by Equations

Other Types of Equations

Solve a Formula for a Variable

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