Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set: 42

Answer

$(-\infty, -9)\cup (-3, +\infty)$

Work Step by Step

First, solve each simple inequality to have: Inequality 1: $x+9 \lt 0 \\x \lt -9$ Inequality 2: $4x \gt -12 x \gt \frac{-12}{4} \\x \gt -3$ This means that the given compound inequality is equivalent to $x \lt -9$ or $x \gt -3$. Graph each simple inequality. (refer to the attached image below) $x \lt -9$ includes all numbers to the left of -9 $\\x \gt -3$ includes all number to the right of -3. The compound inequality involves the conjunction OR, which means that the solution set includes the combined elements of the two inequalities, Thus, the solution set is: $(-\infty, -9) \cup $(-3, +\infty)$
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