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 - Section 4.2 - Compound Inequalities - Exercise Set - Page 272: 50

Answer

$(-\infty,-3]\cup[1,\infty)$. The graph is shown below.

Work Step by Step

The given compound inequality is $\Rightarrow 2x-5\leq-11$ or $5x+1\geq6$. Solve each inequality separately. $\Rightarrow 2x-5\leq-11$ or $5x+1\geq6$. $\Rightarrow 2x\leq-11+5$ or $5x\geq6-1$. $\Rightarrow 2x\leq-6$ or $5x\geq5$. $\Rightarrow x\leq-3$ or $x\geq1$. First graph then take the union of the solution sets of the two inequalities. The graph is shown in the image file. We can write the compound inequality. $x\leq-3$ as $(-\infty,-3]$ and $x\geq1$ as $[1,\infty)$ The union is $(-\infty,-3]\cup[1,\infty)$.
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