## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 75

#### Answer

$(-\infty,-3) \cup (12, \infty)$

#### Work Step by Step

The solutions of $|u|\gt c$ are the numbers that satisfy $u\lt -c$ or $u\gt c.$ --- $|3-\displaystyle \frac{2}{3}x| \gt 5\Rightarrow \left\{\begin{array}{ll} 3-\frac{2}{3}x\lt -5 & \\ or & \\ 3-\frac{2}{3}x \gt 5 & \end{array}\right.$ $\begin{array}{lllll} 3-\frac{2}{3}x\lt -5 & /\times 3 & ...or... & 3-\frac{2}{3}x \gt 5 & /\times 3\\ 9-2x\lt -15 & /-9 & & 9-2x \gt 15 & /-9\\ -2x\lt -24 & /\div(-2) & & -2x \gt 6 & /\div(-2)\\ & (negative!) & & & (negative!)\\ x\gt 12 & & & x \lt -3 & \\ x\in(12,\infty) & & or & x\in(-\infty,-3) & \\ & & & & \end{array}$ Solution set: $(-\infty,-3) \cup (12, \infty)$

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