Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 34


$\left[-\frac{10}{3},-\frac{13}{6}\right]$ Refer to the attached image below for the graph.

Work Step by Step

Subtract 7 to each part to have: $\\-3-7 \le 3x+7-7 \le \frac{1}{2}-7 \\-10 \lt 3x \le \frac{1}{2}-\frac{14}{2} \\-10 \le x \le -\frac{13}{2}$ Divide $3$ to each part to have: $\\\frac{-10}{3} \le x \le \dfrac{-\frac{13}{2}}{3} \\-\frac{10}{3} \le x \le -\frac{13}{6}$ Thus, the solution is $\left[-\frac{10}{3},-\frac{13}{6}\right]$.
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