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.

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.