Absolute Value Inequalities

Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Look at the picture. Which number line corresponds to [-2, 5]?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

• no solution

• all real numbers

• -2 ≤ n ≤ 16

• n ≤ -2 or n ≥ 16

Solve.

|y - 4| ≥ 8

• $\left(-\infty,\ -4\right]\ U\ \left[12,\ \infty\right)$

• $\left[-4,\ 12\right]$
  

• $\left(\infty,\ 4\right]\ U\ \left[-12,\ -\infty\right)$
  

• $\left[-12,\ 4\right]$
  

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.