Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 2 - Functions and Their Graphs - Chapter Review - Cumulative Review - Page 117: 9

Answer

$(-\infty,-2]\cup\left[ \frac{3}{2},\infty\right)$. Refer to the graph below.

Work Step by Step

Step $1$. Remove the absolute value sign using the rule $|a|\ge b\longrightarrow a\ge b \text{ or } a\le b$ to obtain: $$4x+1\ge7\quad \text{or} \quad 4x+1\le -7$$ Step $2$. Solve each inequality. $$\begin{align*} 4x+1&\ge7\\ 4x&\ge6\\ x&\ge \frac{3}{2} \end{align*}$$ $$\begin{align*} 4x+1&\le-7\\ 4x&\le-8\\ x&\le -2 \end{align*}$$ Thus, the solution is $(-\infty, -2] \cup \left[\frac{3}{2}, \infty\right)$. Step $3$. Graph the solution by plotting a bracket at $-2$ and shading the region to its left, then plotting a bracket at $\frac{3}{2}$ then shading the region to its right. Refer to the image below.
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