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: 48

Answer

$(-\infty,-3]\cup(-2,\infty)$

Work Step by Step

Step 1. Rewriting the inequality as $\frac{x+3}{x+2}\geq0$, the boundary points are $x=-3,-2$ Step 2. Using the test points to examine signs across the boundary points, we have $...(+)...(-3)...(-)...(-2)...(+)...$ Thus the solutions are $x\leq-3$ or $x\gt-2$ 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 $(-\infty,-3]\cup(-2,\infty)$
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