Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 4 - Section 4.3 - Equations and Inequalities Involving Absolute Value - Exercise Set - Page 284: 58

Answer

$(-7,9)$. The graph is shown below.

Work Step by Step

The given expression is $\Rightarrow \left | \frac{3x-3}{4}\right |\lt6$ Rewrite the inequality without absolute value bars. $\Rightarrow -6\lt \frac{3x-3}{4}\lt6$ Solve compound inequality. Multiply all three parts by $4$. $\Rightarrow -6(4)\lt \frac{3x-3}{4}(4)\lt6(4)$ Simplify. $\Rightarrow -24\lt 3x-3\lt24$ Add $3$ to all three parts. $\Rightarrow -24+3\lt 3x-3+3\lt24+3$ Simplify. $\Rightarrow -21\lt 3x\lt27$ Divide by $3$ to all three parts. $\Rightarrow \frac{-21}{3}\lt \frac{3x}{3}\lt\frac{27}{3}$ Simplify. $\Rightarrow -7\lt x\lt9$ The solution set $(-7,9)$.
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