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: 54



Work Step by Step

Step 1. Based on the given inequality $\frac{(x+3)(x-2)}{x+1}\leq0$, the boundary points are $x=-3,-1,2$ Step 2. Using test points to examine signs across the boundary points, we have $...(-)...(-3)...(+)...(-1)...(-)...(2)...(+)...$ Thus the solutions are $x\leq-3$ or $-1\lt x\leq2$ with the consideration of the equal sign at the boundary points. 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 $(-\infty,-3]\cup(-1,2]$
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