Introduction to Graphing Absolute Value Inequalities

Solve.
|5x + 7| < 22

• x < -5 ⅘ or x > 3

• -5 ⅘ < x < 3

• -3 < x < 5 ⅘

• x < -3 or x > 5 ⅘

Solve.
|4k + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5

• -4.5 ≤ v ≤ -1.4

• -1.5 ≤ v ≤ 4.5

• v ≤ -1.5 or v ≥ 4.5

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

• all real numbers
• no solution
• 0 < v < 6⁄7
• 0 ≤ v ≤ 6/7

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

• n > 1 or n < -7
• n > -1 or n < -7
• -7 < n < -1
• no solution

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32