Intermediate Algebra (11th edition)

SECTION 2.6 Set Operations and Compound Inequalities 107

Step 2 By taking the union, we obtain the interval 1 - q, - 24 .See FIGURE 26.

–4 –3 –2 –1 0

–4 –3 –2 –1 0

x ≤ –2

x ≤ –3

FIGURE 25

Solving a Compound Inequality with or

Solve the compound inequality, and graph the solution set.

or

Step 1 Solve each inequality individually.

or

or

or

The graphs of these two inequalities are shown in FIGURE 25.

x... - 2 x...- 3

- 4 xÚ 8 5 x...- 15

- 4 x+ 1 Ú 9 5 x+ 3 ...- 12

- 4 x+ 1 Ú 9 5 x+ 3 ...- 12

EXAMPLE 7

–4 –3 –2 –1 0

x ≤ –2

FIGURE 26

NOW TRY
EXERCISE 8
Solve and graph.

or

• 2 x+ 1 7- 9

8 x- 4 Ú 20

–1 0 1 2 3 4 5

NOW TRY
EXERCISE 7
Solve and graph.

• x+ 266 or 6x- 8 Ú 10

–5–4–3 –2 –1 0

–5 –4 –3 –2 –1

x ≥≥ –5

x ≤≤ –3

0

–5 –4 –3 –2 –1 0

FIGURE 27

–5 –4 –3 –2 –1

( –∞∞, ∞∞)

0

FIGURE 28

Step 2 By taking the union, we obtain every real number as a solution, since every

real number satisfies at least one of the two inequalities. The set of all real

numbers is written in interval notation as 1 - q, q 2 and graphed as in FIGURE 28.

NOW TRY

NOW TRY

Solving a Compound Inequality with or

Solve the compound inequality, and graph the solution set.

or

Step 1 Solve each inequality separately.

or

or

or

The graphs of these two inequalities are shown in FIGURE 27.

x... - 3 xÚ- 5

- 2 xÚ 6 4 xÚ- 20

- 2 x+ 5 Ú 11 4 x- 7 Ú- 27

- 2 x+ 5 Ú 11 4 x- 7 Ú- 27

EXAMPLE 8

NOW TRY ANSWERS
7.

8. 1 - q, q 2

1 - 4, q 2