Absolute Value Inequalities

Solve:
 |x + 3| > 8

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

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5
• y ≤ -7 or y ≥ 5
• -5 ≤ y ≤ 7
• y ≤ -5 or y ≥ 7

Solve.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7
• p ≤ -13 or p ≥ 7
• -7 ≤ p ≤ 13
• p ≤ -7 or p ≥ 13

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Solve:  |x - 3| < 8

• x > 5 or x < -11
• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Solve:  |x - 3| > 8

• x > 5 or x < -11
• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Solve: |x + 4| > 10

• x > 6 and x < 10

• x > 6 or x < -14

• all real numbers

• no solution

Solve. |x - 4| > 4

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution