College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises - Page 159: 35


$(-\infty, 1] \cup [2, 3]$

Work Step by Step

Subtract $6x^2+6$ to both sides of the inequality to obtain: $x^3+11x-6x^2-6\le 0 \\x^3-6x^2+11x-6\le0$ Graph the function $y=x^3-6x^2+11x-6$ (refer to the attached image below for the graph) The solution to the given inequality is the set of x-values for which $y\le0$. Notice that $y \le 0$ in the following intervals: $(-\infty, 1]$ and $[2, 3]$
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