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: 66

Answer

$1 \le x \le 4$
1515290074

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 7 \ge g(x) \ge -2 ,$ replace $ g(x) $ with the given function, $ g(x)=3x-5 .$ Then use the properties of inequality to isolate the variable. Finally, graph the solution set. $\bf{\text{Solution Details:}}$ Replacing $ g(x) $ with the given function, then \begin{array}{l}\require{cancel} 7 \ge 3x-5 \ge -2 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 7+5 \ge 3x-5+5 \ge -2+5 \\\\ 12 \ge 3x \ge 3 \\\\ \dfrac{12}{3} \ge \dfrac{3x}{3} \ge \dfrac{3}{3} \\\\ 4 \ge x \ge 1 \\\\ 1 \le x \le 4 .\end{array} The graph includes the points from $1$ (inclusive) to $4$ (inclusive).
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