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: 65


$1\le x \le 3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ 2\le f(x)\le8 ,$ replace $f(x)$ with the given function, $ f(x)=3x-1 .$ Then use the properties of inequality to isolate the variable. Finally, graph the solution set. $\bf{\text{Solution Details:}}$ Replacing $f(x)$ with the given function, then \begin{array}{l}\require{cancel} 2\le 3x-1\le8 .\end{array} Using the properties of inequality, the given is equivalent to \begin{array}{l}\require{cancel} 2\le 3x-1\le8 \\\\ 2+1\le 3x-1+1\le8+1 \\\\ 3\le 3x\le9 \\\\ \dfrac{3}{3}\le \dfrac{3x}{3}\le\dfrac{9}{3} \\\\ 1\le x \le 3 .\end{array} The graph includes the points from $1$ (inclusive) to $3$ (inclusive).
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