Inequalities Involving Absolute Value

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

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

Solve: | 3x - 9 | < 3

• x< - 10 or x > - 2

• -10 < x < - 2

• x < 2 or x > 4

• 2 < x < 4

Solve: |-9v| < 54

• -6<v<6

• v<-6 or v>6

• v=6 or v=-6

• 6>v<6

Solve. |c + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers