1.5 Solving Absolute Value Inequalities

Solve.

• -1 < r or r < 9

• -1 < r < 9

• r < 9

• -1 < r

Solve.

• b < -8

• b > -8

• All real numbers

• No solution

• r > 11/4 or r < 9/4

• r > 5 or r ≤ 0

• r > 5 or r < 0

• r < -5 or r > 0

|x-10|+7 > 15

• no solution

• x > -2 or x < -8

• x > 18 or x < 2

• all real numbers

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Solve the following inequality:

| x − 2 | > 3

• 2 < x < 10

• x < 2 or x > 10

• −1 < x < 5

• x < −1 or x > 5

Solve the following inequality:

| 2w − 1 | < 11

• No Solution

• All Real Numbers

• −5 < w < 6

• −6 < w < 5

Solve the following inequality:

|10 + 4x| < 14

• x < 1 and x > −6

• x < 1 or x > −6

• x < 6 and x > −6

• x < 1 or x > −1

Solve the following inequality:

|3x + 6| ≥ 15

• x ≥ 3 or x ≤ −3

• x ≤ 7 and x ≤ −3

• x ≥ 7 and x ≤ −7

• x ≤ −7 or x ≥ 3