Intermediate Algebra (11th edition)

106 CHAPTER 2 Linear Equations, Inequalities, and Applications

Solving a Compound Inequality with or

Solve the compound inequality, and graph the solution set.

or

Step 1 Solve each inequality individually.

or

or

The graphs of these two inequalities are shown in FIGURE 23.

x 61 xÚ 3

4 x 64

6 x- 462 x - 3 x...- 9

6 x- 46 2 x - 3 x...- 9

EXAMPLE 6

The set of points

in either of the

graphs represents

the union.

–1 0

0

1

1

2

2

3

3

4

–1 4

x < 1

x ≥ 3

FIGURE 23

–1 0 1 2 3 4

(–∞, 1) ∪ [3, ∞)

FIGURE 24

NOW TRY
EXERCISE 6
Solve and graph.

• 12 x...- 24 or x+ 968

–2 –1 0 1 2 3

Solving a Compound Inequality with or

Step 1 Solve each inequality individually.

Step 2 Since the inequalities are joined with or,the solution set of the com-

pound inequality includes all numbers that satisfy either one of the

two inequalities in Step 1 (the union of the solution sets).

CAUTION When inequalities are used to write the solution set in Example 6,it

mustbe written as

or

which keeps the numbers 1 and 3 in their order on the number line. Writing

, which translates using and, would imply that which is FALSE.

There is no other way to write the solution set of such a union.

3 ... x 61 3 ... 1,

x 6 1 xÚ3,

Step 2 Since the inequalities are joined with or,find the union of the two solution

sets. The union is shown in FIGURE 24and is written

1 - q, 1 2 ́ 3 3, q 2.

NOW TRY

Remember to

reverse the

inequality symbol.

OBJECTIVE 4 Solve compound inequalities with the word or.Use the fol-

lowing steps to solve a compound inequality such as “ 6 x- 462 xor - 3 x...- 9 .”

NOW TRY ANSWER

6. 1 - q, - 12 ́ 3 2, q 2