Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 4 - Mid-Chapter Check Point - Page 286: 12

Answer

$(-\infty,-1)\cup(-\frac{1}{5},\infty)$.

Work Step by Step

The given expression is $\Rightarrow \left | 5x+3\right |\gt2$ Rewrite the inequality without absolute value bars. $\Rightarrow 5x+3\lt-2$ or $5x+3\gt2$ Solve each inequality separately. Subtract $3$ from all parts. $\Rightarrow 5x+3-3\lt-2-3$ or $5x+3-3\gt2-3$ Simplify. $\Rightarrow 5x\lt-5$ or $5x\gt-1$ Divide all parts by $5$. $\Rightarrow \frac{5x}{5}\lt\frac{-5}{5}$ or $\frac{5x}{5}\gt\frac{-1}{5}$ Simplify. $\Rightarrow x\lt-1$ or $x\gt-\frac{1}{5}$ The solution set is less than $-1$ or greater than $-\frac{1}{5}$. The interval notation is $(-\infty,-1)\cup(-\frac{1}{5},\infty)$.
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