Intermediate Algebra for College Students (7th Edition)

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

Chapter 5 - Cumulative Review Exercises - Page 402: 5

Answer

$(-\infty,-2]\cup[7,\infty)$.

Work Step by Step

The given inequality is an absolute value inequality in the form $|a|\geq c$ which can be written without absolute value bars as $a\leq -b$ or $a\geq b.$ Rewrite the fiven inequality. $\Rightarrow 2x-5\leq-9$ or $2x-5\geq9$ Add $5$ to all parts. $\Rightarrow 2x-5+5\leq-9+5$ or $2x-5+5\geq9+5$ Simplify. $\Rightarrow 2x\leq-4$ or $2x\geq14$ Divide all parts by $2$. $\Rightarrow \frac{2x}{2}\leq\frac{-4}{2}$ or $\frac{2x}{2}\geq\frac{14}{2}$ Simplify. $\Rightarrow x\leq-2$ or $x\geq7$ The solution set is the set of real numbers less than or equal to $-2$ or greater than or equal to $7$. The interval notation is $(-\infty,-2]\cup[7,\infty)$. We used square brackets because $-2$ and $7$ belong to the solution set.
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