Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1-9 - Cumulative Review: 9

Answer

$-2\le x \le \dfrac{10}{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ |3x-2|\le8 ,$ use the definition of less than (less than or equal to) absolute value inequality. Then use the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to \begin{array}{l}\require{cancel} -8\le 3x-2 \le8 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -8\le 3x-2 \le8 \\\\ -8+2\le 3x-2+2 \le8+2 \\\\ -6\le 3x \le10 \\\\ -\dfrac{6}{3}\le \dfrac{3x}{3} \le \dfrac{10}{3} \\\\ -2\le x \le \dfrac{10}{3} .\end{array} Hence, the solution set $ -2\le x \le \dfrac{10}{3} .$
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