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 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 590: 59


$-3\le x \le 2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -10\le3x-1\le5 .$ Then graph. In the graph above, a hollowed dot is used for $\lt$ or $\gt$. A shaded dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} -10\le3x-1\le5 \\\\ -10+1\le3x-1+1\le5+1 \\\\ -9\le3x\le6 \\\\ -\dfrac{9}{3}\le\dfrac{3x}{3}\le\dfrac{6}{3} \\\\ -3\le x \le 2 .\end{array} The graph includes the points from $-3$ (inclusive) to $2$ (inclusive).
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