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 - Page 94: 43


$(-\infty, +\infty)$

Work Step by Step

First, solve each simple inequality to have: Inequality 1: $3(x-1) \lt 12 \\3x-3 \lt 12 \\3x \lt 12+3 \\3x \lt 15 \\x \lt \frac{15}{3} \\x \lt 5$ Inequality 2: $x+7 \gt 10 x \gt 10-7 \\x \gt 3$ This means that the given compound inequality is equivalent to $x \lt 5$ or $x \gt 3$. Graph each simple inequality. (refer to the attached image below) $x \lt 5$ includes all numbers to the left of 5 $\\x \gt 3$ 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: $(-\infty, +\infty)$
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