Intermediate Algebra (11th edition)

2.6 Set Operations and Compound

Inequalities

Solving a Compound Inequality

Step 1 Solve each inequality in the compound inequality
individually.

Step 2 If the inequalities are joined with and, then the
solution set is the intersection of the two individ-
ual solution sets.

If the inequalities are joined with or, then the

solution set is the union of the two individual

solution sets.

Solve and

The solution set is

Solve or

The solution set is

–1 012345

1 - q, 0 4 ́ 3 4, q 2.

xÚ 4 x...0.

–1 0 1 2 3

1 1, 3 2.

x 71 and x 63

x+ 172 and 2 x 66

x+ 172 2 x 6 6.

CONCEPTS EXAMPLES

126 CHAPTER 2 Linear Equations, Inequalities, and Applications

2.7 Absolute Value Equations and

Inequalities

Solving Absolute Value Equations and Inequalities
Let kbe a positive number.

To solve solve the following compound
equation.

To solve solve the following compound
inequality.

axb>k or axb<k

axb>k,

axbk or axbk

axbk,

Solve

Add 7.

The solution set is.

Solve

Add 7.

The solution set is

082 46 10

1 - q, 4 2 ́ 1 10, q 2.

x 710 or x 64

x- 773 or x- 7 6- 3

|x- 7 | 7 3.

082 46 10

5 4, 10 6

x= 10 or x= 4

x- 7 = 3 or x- 7 =- 3

|x- 7 |=3.

To solve solve the following compound
inequality.

To solve an absolute value equation of the form

solve the following compound equation.

axbcxd or axb 1 cxd 2

axbcxd,

k<axb<k

axb<k, Solve

Add 7.

The solution set is

Solve

The solution set is E^43 , 8F.

x=

4

3

3 x= 4

x= 8 x+ 2 =- 2 x+ 6

x+ 2 = 2 x- 6 or x+ 2 =- 12 x- 62

|x+ 2 |=| 2 x- 6 |.

0821046

1 4, 10 2.

4 6 x 610

• 36 x- 763

|x- 7 | 6 3.