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: 55

Answer

$(-\infty,-5)\cup(-3,\infty)$

Work Step by Step

Step 1. Rewrite the inequality as $\frac{x+1}{x+3}-2\lt0$, which gives $\frac{x+1-2x-6}{x+3}\lt0$, $\frac{-x-5}{x+3}\lt0$, and $\frac{x+5}{x+3}\gt0$ Thus the boundary points are $x=-5,-3$ Step 2. Using test points to examine signs across the boundary points, we have $...(+)...(-5)...(-)...(-3)...(+)...$ Thus the solutions are $x\lt-5$ or $ x\gt-3$ 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 $(-\infty,-5)\cup(-3,\infty)$
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