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: 9

Answer

$(-\infty,\infty)$.

Work Step by Step

The given compound inequality is $3x-2\gt-8$ or $2x+1\lt9$ Solve each inequality separately. $\Rightarrow 3x-2\gt-8$ or $2x+1\lt9$ $\Rightarrow 3x-2+2\gt-8+2$ or $2x+1-1\lt9-1$ $\Rightarrow 3x\gt-6$ or $2x\lt8$ $\Rightarrow \frac{3x}{3}\gt\frac{-6}{3}$ or $\frac{2x}{2}\lt\frac{8}{2}$ $\Rightarrow x\gt-2$ or $x\lt4$ First graph then take the union of the two inequalities. We can write the compound inequality. $x\gt-2$ as $(-2,\infty)$ and $x\lt4$ as $(-\infty,4)$ The union is $(-\infty,4)\cup(-2,\infty)=(-\infty,\infty)$. The graph is shown below.
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