Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.7 - Polynomial and Rational Inequalities - Exercise Set - Page 413: 59

Answer

$(-\infty,-6]\cup(-2,\infty)$

Work Step by Step

Step 1. Rewrite the inequality as $\frac{x-2}{x+2}-2\leq0$ which gives $\frac{x-2-2x-4}{x+2}\leq0$, $\frac{-x-6}{x+2}\leq0$ and $\frac{x+6}{x+2}\geq0$ Thus the boundary points are $x=-6,-2$ Step 2. Using test points to examine signs across the boundary points, we have $...(+)...(-6)...(-)...(-2)...(+)...$ Thus the solutions are $x\leq-6$ plus $x\gt-2$ Step 3. We can express the solutions on a real number line as shown in the figure. Step 4. We can express the solutions in interval notation as $(-\infty,-6]\cup(-2,\infty)$
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