College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises - Page 148: 28

Answer

$\left[-\dfrac{4}{5}, \dfrac{9}{5}\right]$ Refer to the image below for the graph.

Work Step by Step

Add $4$ to each part of the inequality to obtain: $\begin{array}{ccccc} &-8+4 &\le &5x-4+4 &\le &5+4 \\&-4 &\le &5x &\le &9 \end{array}$ Divide $5$ to each part of the inequality to obtain: $\begin{array}{ccccc} &\dfrac{-4}{5} &\le &\dfrac{5x}{5} &\le &\dfrac{9}{5} \\&\dfrac{-4}{5} &\le &x &\le &\dfrac{9}{5} \end{array}$ Thus, the solution set is $\bf\left[\frac{-4}{5}, \frac{9}{5}\right]$. To graph this solution set, plot solid dots at $\dfrac{-4}{5}8$ (or $-0.8$) and $\dfrac{9}{5}$ (or $ 1.8$) then shade the region in between. (refer to the attached image in the answer part above for the graph)
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