College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises - Page 148: 34


$(-\infty, -4] \cup [5, +\infty)$ Refer to the image below for the graph.

Work Step by Step

First step is to find the zeros of each factor. The factors $x-5$ and $x+4$ are zero when $x=5$ and $x=-4$, respectively. Next step is to find the intervals. The zeros $-4$ and $5$ divide the number line into three intervals, namely: $(-\infty, -4), (-4, 5), \text{ and } (5, +\infty)$. $\bf\text{Make a table of signs}.$ (refer to the attached image below) $\bf\text{Solve}$ From the table of signs, it can be seen that $(x-5)(x+4)\ge 0$ in the intervals $(-\infty, -4)$ and $(5, +\infty)$. The inequality involves $ge$ therefore the endpoints $-4$ and $5$ are part of the solution set. Thus, the solution set is $(-\infty, -4] \cup [5, +\infty)$. To graph this, plot holes at $-4$ and $5$ then shade the region to the left of $-4$ and the region to the right of 5. (refer to the attached image in the answer part above)
Small 1509721323
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.