Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Review Exercises - Page 432: 87

Answer

$(-3,0)\cup(1,\infty)$

Work Step by Step

Step 1. Rewriting and factor the inequality as $x^3+2x^2-3x=x(x^2+2x-3)=x(x+3)(x-1)\gt0$, we can identify the boundary points as $x=-3,0,1$ Step 2. Use test points to examine the signs of the left side across the boundary points; we have $...(-)...(-3)...(+)...(0)...(-)...(1)...(+)...$; thus the solutions are $(-3,0)\cup(1,\infty)$ Step 3. We can graph the solution on a real number line as shown in the figure.
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