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

Answer

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