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: 50

Answer

$[-\frac{5}{3}, 3)$

Work Step by Step

Step 1. Rewrite the inequality as $\frac{3(x+5/3)}{2(x-3)}\leq0$; the boundary points are $x=-5/3,3$ Step 2. Using test points to examine signs across the boundary points, we have $...(+)...(-5/3)...(-)...(3)...(+)...$ Thus the solutions are $-\frac{5}{3}\leq x\lt3$ 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 $[-\frac{5}{3}, 3)$
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