Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set - Page 600: 92


Upon substitution, the given inequality with the given value of the variable ends with a FALSE statement.

Work Step by Step

Substituting $x=-7$ in the inequality $|x|\lt5$ results to \begin{array}{l}\require{cancel} |x|\lt5 \\\\ |-7|\lt5 \\\\ 7\lt5 \text{ (FALSE)} .\end{array} Since the substitution above ended with a FALSE statement, then $x=-7$ is not a solution to the inequality.
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