Solve Absolute Inequalities and Graph

Solve.
|c + 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.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3

• c < -5 1/3  or c > 2 2/3

• c < 5 1/3 or c > -2 2/3

• -5 1/3 < c < 2 2/3

Solve.
3|d - 4| = 12

• d = -8 or d = 0

• no solution

• d = 8 or d = 0

• d = 40 or d = 32

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

Solve.
6 - 2|m -3| > -4

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

A golf ball manufacturer puts 390 golf balls in each box. The box can be off by 6 golf balls. Write an inequality that displays the acceptable amount of golf balls that can be in a box.

• |x - 6| < 390

• |x - 6| ≤ 390

• |x - 390| < 6

• |x - 390| ≤ 6