College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Cumulative Review - Page 196: 14

Answer

$(-\infty, -5) \cup (1, +\infty)$ Refer to the image below for the graph.
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Work Step by Step

RECALL: $|x| \gt a \longrightarrow x \gt a \text{ or } x \lt -a$ Use the rule above to obtain: $2+x \gt 3 \color{blue}{\text{ or }} 2+x \lt -3$ Solve each inequality to obtain: $2+x\gt 3 \\x \gt 3-2 \\x \gt 1$ or $2+x \lt -3 \\x \lt -3-2 \\x \lt -5$ In interval notation, the solution set is: $(-\infty, -5) \cup (1, +\infty)$ To graph the inequalities, plot holes at $-5$ and $1$, then shade the region to the right of $1$ and the region to the left of $-5$.
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