Absolute Value Inequalities

Solve.
|2t + ⅔| < 4

• -5/3 < t < 7/3

• t > 7/3 or t < -5/3

• -7/3 < t < 5/3

• t > 5/3 or t < -7/3

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.

|4v + 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.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve.

|-3f| ≥ 6.3

• -18.9 ≤ f ≤ 18.9

• no solution

• f ≤ -2.1 or f ≥ 2.1

• -2.1 ≤ f ≤ 2.1

Solve.
|4m + 9| ≥ 21

• -7.5 ≤ m ≤ 3

• m ≤ -7.5 or m ≥ 3

• -3 ≤ m ≤ 7.5

• m ≤ -3 or m ≥ 7.5

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

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

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

The rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Which inequality represents represents the acceptable number of words?

• |x - 30| < 500

• |x - 30| ≤ 500

• |x - 500| < 30

• |x - 500| ≤ 30