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: 33

Answer

$(-2, 3)$ 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 $x+2$ and $x-3$ are zero when $x=-2$ and $x=3$, respectively. Next step is to find the intervals. The zeros $-2$ and $3$ divide the number line into three intervals, namely: $(-\infty, -2), (-2, 3), \text{ and } (3, +\infty)$. $\bf\text{Make a table of signs}.$ (refer to the attached image below) $\bf\text{Solve}$ From the table of signs, it can be seen that $(x+2)(x-3)\lt 0$ in the interval $(-2, 3)$. The inequality involves $lt$ therefore the endpoints $-$ and $3$ are not part of the solution set. Thus, the solution set is $(-2, 3)$. To graph this, plot holes at $-2$ and $3$ then shade the region between them. (refer to the attached image in the answer part above)
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