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 592: 110


$-4\lt x\le 1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ x-10\lt5x+6\le x+10 .$ 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 given is equivalent to \begin{array}{l}\require{cancel} x-10\lt5x+6\le x+10 \\\\ x-10-x\lt5x+6-x\le x+10-x \\\\ -10\lt4x+6\le 10 \\\\ -10-6\lt4x+6-6\le 10-6 \\\\ -16\lt4x\le 4 \\\\ \dfrac{-16}{4}\lt\dfrac{4x}{4}\le \dfrac{4}{4} \\\\ -4\lt x\le 1 .\end{array} The graph consists of all points from $-4$ (exclusive) to $1$ (inclusive).
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