Absolute Value Inequality Functions

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 - 3| > 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

Describe the first step in solving the absolute value inequality

• Add 5 on both sides

• Divide both sides by -5

• Set up two inequalities

• no solution

Solve:  |2x + 1| ≤ 19

• x ≥ 9 or x ≤ -10

• -10 ≤ x ≤ 9

• x ≥ 10 or x ≤ -9

• -9 ≤ x ≤ 10

Solve:  |2x - 1| ≥ 19

• x ≥ 9 or x ≤ -10

• -10 ≤ x ≤ 9

• x ≥ 10 or x ≤ -9

• -9 ≤ x ≤ 10

Solve:  |k| < 8

• x > 8 or x < -8

• -8 < k < 8

• No solution

• Infinite solution

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32