Absolute Value Inequalities

Solve.
3|d - 4| = 12

• d = -8 or d = 0

• no solution

• d = 8 or d = 0

• d = 40 or d = 32

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

Which graph represents the solution to the absolute-value inequality:

I 2x - 11 I < 21

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Answer explanation

Remember what sort of graph < means for absolute-value.

Which graph represents the solution to the absolute-value inequality:

I 3x + 9 I > 27

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Answer explanation

Remember what sort of graph > means for absolute-value.

Solve:
|x + 3| > - 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or

What kind of compound inequality is this?

• AND compound inequality

• OR compound inequality

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

Solve.
-5|x - 4| > -20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers