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: 64


$18\le x \le 24$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -10\le \dfrac{x+6}{-3} \le -8 .$ 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} -10\le \dfrac{x+6}{-3} \le -8 \\\\ -3(-10)\le -3\left( \dfrac{x+6}{-3} \right) \le -3(-8) \\\\ 30\ge x+6 \ge 24 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 30\ge x+6 \ge 24 \\\\ 30-6\ge x+6-6 \ge 24-6 \\\\ 24\ge x \ge 18 \\\\ 18\le x \le 24 .\end{array} The graph includes the points from $18$ (inclusive) to $24$ (inclusive).
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