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: 33

Answer

$(-\infty,2)\cup(2,\frac{7}{2})$

Work Step by Step

Step 1. Rewrite the inequality as $(x-2)^2(x-\frac{7}{2})\lt0$ The boundary points are: $x=2,\frac{7}{2}$ Step 2. Using test points to examine signs across the boundary points, we have $...(-)...(2)...(-)...(\frac{7}{2})...(+)...$ Thus the solutions are: $x\lt\frac{7}{2}$ plus $x\ne2$ 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 $(-\infty,2)\cup(2,\frac{7}{2})$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.