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 95: 62


The solution is $(-3,0]$

Work Step by Step

$5x\le0$ and $-x+5\lt8$ Solve the first inequality: $5x\le0$ Take $5$ to divide the right side: $x\le\dfrac{0}{5}$ $x\le0$ Expressing in interval notation: $(-\infty,0]$ Solve the second inequality: $-x+5\lt8$ Take $5$ to the right side: $-x\lt8-5$ $-x\lt3$ Change the sign on both sides and reverse the direction of the inequality sign: $x\gt-3$ Expressing in interval notation: $(-3,\infty)$ Since the compound inequality is formed by the word "and", the solution is composed by the numbers that satisfy both inequalities at the same time: The solution is $(-\infty,0]\cap(-3,\infty)$ or $(-3,0]$
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