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 - Test: Chapter 9 - Page 624: 16


$-3\le x \le 1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given, $ 1\le 3-2x \le 9 .$ Then graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 1\le 3-2x \le 9 \\\\ 1-3\le 3-2x-3 \le 9-3 \\\\ -2\le -2x \le 6 .\end{array} Dividing 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 -2x \le 6 \\\\ \dfrac{-2}{-2}\le \dfrac{-2x}{-2} \le \dfrac{6}{-2} \\\\ 1\ge x \ge -3 \\\\ -3\le x \le 1 .\end{array}
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