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 414: 90

Answer

$(-\infty,-3)\cup[8,\infty)$
1582380485

Work Step by Step

Step 1. Rewrite the inequality as $\frac{x+2}{x-3}-2\leq0$, $\frac{x+2-2x+6}{x-3}\leq0$, $\frac{-x+8}{x-3}\leq0$, and $\frac{x-8}{x-3}\geq0$; then graph the function $f(x)=\frac{x-8}{x-3}$ as shown in the figure. Step 2. The zeros of the function can be identified as $x=8$ Step 3. We can identify the regions where $f(x)\geq0$ as $(-\infty,-3)\cup[8,\infty)$
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