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: 62


$-7\le x \le 7$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 3\ge \dfrac{x-1}{2} \ge -4 .$ Then graph. In the graph above, a hollowed dot is used for $\lt$ or $\gt$. A shaded dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 3\ge \dfrac{x-1}{2} \ge -4 \\\\ 2(3)\ge 2\left( \dfrac{x-1}{2} \right) \ge 2(-4) \\\\ 6\ge x-1 \ge -8 \\\\ 6+1\ge x-1+1 \ge -8+1 \\\\ 7\ge x \ge -7 \\\\ -7\le x \le 7 .\end{array} The graph includes the points from $-7$ (inclusive) to $7$ (inclusive).
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