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: 30

Answer

$\left[-\dfrac{10}{3}, -\dfrac{13}{6}\right]$ Refer to the image below for the graph.
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Work Step by Step

Subtract $7$ to each part of the inequality to obtain: $\begin{array}{ccccc} &-3-7 &\le &3x+7-7 &\le &\frac{1}{2}-7 \\&-10 &\le &3x &\le &\frac{1}{2}-\frac{14}{2} \\&-10 &\le &3x &\le &-\frac{13}{2} \end{array}$ Divide $3$ to each part of the inequality to obtain: $\begin{array}{ccccc} &\dfrac{-10}{3} &\le &\dfrac{3x}{3} &\le &\dfrac{-\frac{13}{2}}{3} \\&-\dfrac{10}{3} &\le &x &\le &-\dfrac{13}{6} \end{array}$ Thus, the solution set is $\bf\left[-\dfrac{10}{3}, -\dfrac{13}{6}\right]$. To graph this solution set, plot solid dots at $-\dfrac{10}{3}$ and $-\dfrac{13}{6}$ then shade the region in between. (refer to the attached image in the answer part above for the graph)
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