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: 91

Answer

$(-4,-1)\cup[2,\infty)$
1582381192

Work Step by Step

Step 1. Rewrite the inequality as $\frac{1}{x+1}-\frac{2}{x+4}\leq0$, $\frac{x+4-2x-2}{(x+1)(x+4)}\leq0$, $\frac{-x+2}{(x+1)(x+4)}\leq0$, and $\frac{x-2}{(x+1)(x+4)}\geq0$; then graph the function $f(x)=\frac{x-2}{(x+1)(x+4)}$ as shown in the figure. Step 2. We can identify a zero as $x=2$, asymptotes as $x=-4$ and $x=-1$ Step 3. We can identify the regions where $f(x)\geq0$ as $(-4,-1)\cup[2,\infty)$
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