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 - Review Exercises: Chapter 9 - Page 623: 22


$-\dfrac{5}{4}\lt x \lt \dfrac{5}{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given, $ -15\lt -4x-5\lt0 .$ 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 equality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -15\lt -4x-5\lt0 \\\\ -15+5\lt -4x-5+5\lt0+5 \\\\ -10\lt -4x \lt 5 .\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} \dfrac{-10}{-4}\lt \dfrac{-4x}{-4} \lt \dfrac{5}{-4} \\\\ \dfrac{5}{2}\gt x \gt -\dfrac{5}{4} \\\\ -\dfrac{5}{4}\lt x \lt \dfrac{5}{2} .\end{array}
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