Intermediate Algebra (11th edition)

OBJECTIVE 1 Solve linear inequalities by using the addition property. We

solve an inequality by finding all numbers that make the inequality true. Usually, an

inequality has an infinite number of solutions. These solutions, like solutions of

equations, are found by producing a series of simpler related equivalent inequalities.

Equivalent inequalitiesare inequalities with the same solution set.

We use two important properties to produce equivalent inequalities. The first is

the addition property of inequality.

92 CHAPTER 2 Linear Equations, Inequalities, and Applications

Addition Property of Inequality

For all real numbers A, B, and C, the inequalities

and are equivalent.

That is, adding the same number to each side of an inequality does not change the

solution set.

A<B AC<BC

Using the Addition Property of Inequality

Solve , and graph the solution set.

Add 7.

Combine like terms.

CHECK Substitute for xin the equation

Related equation

Let

✓ True

This shows that is the boundary point. Now test a number on each side of

to verify that numbers less than make the inequality true. We choose and

Let Let

False ✓ True

is not in the solution set. is in the solution set.

The check confirms that 1 - q, - 52 ,graphed in FIGURE 9, is the correct solution set.

- 4 - 6

- 11 6- 12 - 13 6- 12

- 6 - 76 x=-6.

?

- 4 - 76 x=-4. - 12

?

- 12

x- 7 6- 12

- 6.

- 5 - 4

- 5 - 5

- 12 =- 12

- 5 - 7 - 12 x=-5.

x- 7 =- 12

- 5 x- 7 = -12.

x6- 5

x- 7 + 7 6- 12 + 7

x- 7 6- 12

x- 7 6- 12

EXAMPLE 1

–10 –5 0

FIGURE 9 NOW TRY

As with equations, the addition property can be used to subtractthe same number

from each side of an inequality.

NOW TRY
EXERCISE 1
Solve and
graph the solution set.

x- 10 7-7,

NOW TRY ANSWER

1. 1 3, q 2

01234 5