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: 63


$-32\le x \le 8$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -2\le \dfrac{x+2}{-5} \le 6 .$ Then graph. $\bf{\text{Solution Details:}}$ Multiplying both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -2\le \dfrac{x+2}{-5} \le 6 \\\\ -5(-2)\le -5\left( \dfrac{x+2}{-5} \right) \le -5(6) \\\\ 10\ge x+2 \ge -30 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 10\ge x+2 \ge -30 \\\\ 10-2\ge x+2-2 \ge -30-2 \\\\ 8\ge x \ge -32 \\\\ -32\le x \le 8 .\end{array} The graph includes the points from $-32$ (inclusive) to $8$ (inclusive).
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