Solve Absolute Value Inequalities

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

Solve:
|x + 3| > - 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

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.
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

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

A company makes boxes of crackers that should weigh 213g. A quality control inspector randomly selects boxes to weigh.  Any box that varies from the weight by more than 5g is sent back. What is an equation that shows the range of allowable weights for a box of crackers and what is the range?

• |w - 213| ≤ 5,         208 ≤ w ≤ 218

• |w - 213| ≤ 5,                   0 ≤ w ≤ 10

• |w - 5| ≤ 213,         208 ≤ w ≤ 218

• |w - 5| ≤ 213,                   0 ≤ w ≤ 10