4-2 Solving Inequalities Using Addition and Subtraction

[Pages:6]4-2

1. Plan

Objectives

1 To use addition to solve inequalities

2 To use subtraction to solve inequalities

Examples

1 Using the Addition Property of Inequality

2 Solving and Checking Solutions

3 Using the Subtraction Property of Inequality

4 Real-World Problem Solving

Math Background

Students may have used a balance scale to model equations. Here it may help them to solve inequalities if they refer to an unbalanced scale.

More Math Background: p. 198C

Lesson Planning and Resources

See p. 198E for a list of the resources that support this lesson.

PowerPoint

Bell Ringer Practice

Check Skills You'll Need For intervention, direct students to: Adding Rational Numbers Lesson 2-1: Example 2 Extra Skills and Word

Problems Practice, Ch. 2 Solving One-Step Equations Review p. 118: Example 1

4-2

Solving Inequalities Using

Addition and Subtraction

What You'll Learn

? To use addition to solve

inequalities

? To use subtraction to solve

inequalities

. . . And Why

To solve a problem involving safe loads, as in Example 4

Check Skills You'll Need

GO for Help Lesson 2-1 and Review page 118

Complete each statement with R, , or S.

S

R

1. 23 1 4 25 1 4 2. 23 1 6 4 1 6

S 3. 23.4 1 2 23.45 1 2

Solve each equation.

4. x 2 4 5 5 9

5. n 2 3 5 25 ?2 6. t 1 4 5 25 ?9

7.

k

1

2 3

5

5 6

1 6

New Vocabulary ? equivalent inequalities

1 Part 1 Using Addition to Solve Inequalities

Equivalent inequalities are inequalities with the same solutions. For example, x 1 4 , 7 and x , 3 are equivalent inequalities.

Key Concepts

x + 4 < 7

x < 3

You can add the same value to each side of an inequality, just as you did with equations.

Property

Addition Property of Inequality

For every real number a, b, and c, if a . b, then a 1 c . b 1 c;

if a , b, then a 1 c , b 1 c.

Examples 3 . 1, so 3 1 2 . 1 1 2.

25 , 4, so 25 1 2 , 4 1 2.

This property is also true for $ and #.

1 EXAMPLE Using the Addition Property of Inequality

Solve x 2 3 , 5. Graph the solution.

x 2 3 1 3 , 5 1 3 Add 3 to each side.

x,8

Simplify.

1 0 1 2 3 4 5 6 7 8 9 10

Quick Check 1 Solve m 2 6 . 24. Graph your solution. m S 2;

01 2345

206 Chapter 4 Solving Inequalities

206

Special Needs L1 To help students understand infinity, use the number line in Example 2. Ask: What number is to the right of 20? 21 of 21? 22 Then ask: Will there ever be a number that does not have yet another number to its right? No

learning style: visual

Below Level L2 Present students with several pairs of inequalities and their solutions. Have students take turns explaining what was done to each inequality to produce its solution.

learning style: verbal

Vocabulary Tip

The word infinite indicates that the number of solutions is unlimited. The solutions cannot be listed.

An inequality has an infinite number of solutions, so it is not possible to check all the solutions. You can check your computations and the direction of the inequality symbol. The steps below show how to check that x < 8 describes the solutions to Example 1.

Step 1 Check the computation. See if 8 is the solution to the equation x 2 3 5 5. x2355 8 2 3 0 5 Substitute 8 for x. 555

Step 2 Check the inequality symbol. Choose any number less than 8 and substitute it into x 2 3 , 5. In this case, use 7. x23 ................
................

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