Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 90


$(-\infty, \infty)$

Work Step by Step

Using the properties of inequality, the given expression, $ 7|x+2|+5\gt4 ,$ is equivalent to \begin{array}{l}\require{cancel} 7|x+2|\gt4-5 \\\\ 7|x+2|\gt-1 \\\\ |x+2|\gt-\dfrac{1}{7} .\end{array} The left side of the inequality is always a nonnegative number. This is always greater than the negative value at the right. Hence, the solution set is $ (-\infty, \infty) .$
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