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: 44


The solution is $(-\infty,\infty)$

Work Step by Step

$5(x-1)\ge-5$ or $5+x\le11$ Solve the first inequality. $5(x-1)\ge-5$ Evaluate the product on the left side: $5x-5\ge-5$ Take $5$ to the right side: $5x\ge-5+5$ $5x\ge0$ Take $5$ to divide the right side: $x\ge\dfrac{0}{5}$ $x\ge0$ Expressing in interval notation: $[0,\infty)$ Solve the second inequality: $5+x\le11$ Take $5$ to the right side: $x\le11-5$ $x\le6$ Expressing the solution in interval notation: $(-\infty,6]$ Since the compound inequality is formed by the word "or", the solution is formed by the solution of both inequalities: $(-\infty,6]\cup[0,\infty)$ or $(-\infty,\infty)$
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