# Absolute Value Equations and Inequalities Worksheet

Absolute Value Equations and Inequalities Worksheet
• Page 1
1.
Solve the inequality, | 9 - $x$ | < 5.
 a. { $x$: 4 < $x$ < 14 } b. { $x$: $x$ < 4 or $x$ > 14 } c. { $x$: $x$ < - 14 or $x$ > 4 } d. { $x$: - 14 < $x$ < 4 }

2.
Solve the inequality, | $x$ - 3 | > 4.
 a. { $x$: $x$ < 1 or $x$ > 7 } b. { $x$: $x$ < - 7 or $x$ > 1 } c. { $x$: $x$ < -1 or $x$ > 7 } d. None of the above

3.
Solve the inequality, | $x$ + 2 | - 3 < 5.
 a. { $x$: - 10 < $x$ < 6 } b. { $x$: 6 < $x$ < 10 } c. { $x$: - 10 < $x$ < - 6 } d. { $x$: - 2 < $x$ < 8 }

4.
Solve the inequality, | 2$x$ | < 16.
 a. { $x$: - 8 ≤ $x$ ≤ 8 } b. { $x$: - 8 < $x$ < 8 } c. { $x$: 0 < $x$ < 8 } d. { $x$: - 8 < $x$ < 0 }

5.
Solve the inequality, | $x$ | + 3 < 10.
 a. { $x$: - 7 < $x$ < 7 } b. { $x$: - 13 < $x$ < 13 } c. { $x$: 7 < $x$ < 13 } d. None of the above

6.
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
3[2$y$ + (3$y$ - 1)] ≥ 5(2$y$ + 1)
 a. {$y$: $y$ ≤ 1.6} b. {$y$: $y$ ≥ 1.6} c. {$y$: $y$ ≤ - 1.6} d. {$y$: $y$ ≥ 2.6}

7.
Identify the graph that the inequality represents.

7$r$ - 9 < 4$r$ + 30

 a. Graph A b. Graph B c. Graph C d. Graph D

8.
Solve for $x$.
5$a$$x$ + 8$b$ < 2$a$$x$ - 6$b$, $a$ < 0
 a. {$x$: $x$ > $\frac{14b}{3a}$ } b. {$x$: $x$ > - $\frac{14b}{3a}$ } c. {$x$: $x$ < $\frac{14b}{3a}$ } d. {$x$: $x$ < - $\frac{14b}{3a}$ }

9.
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
7 [2$x$ - ($x$ + 7)] < 3 (2$x$ - 3)
 a. {$x$: $x$ < - 40} b. {$x$: $x$ < - 58} c. {$x$: $x$ < 58} d. {$x$: $x$ < 40}

15 < 3 (2$n$ + 1) + 24, $n$ is a real number.
 a. $n$ < - 2, Graph A b. $n$ > - 2, Graph B c. $n$ ≥ - 2, Graph C d. $n$ ≤ - 2, Graph D