Intermediate Algebra: Connecting Concepts through Application

$-5\lt x\lt5$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $|x|\lt5 ,$ use the definition of absolute value inequality. Then graph the solution. In the graph a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to \begin{array}{l}\require{cancel} -5\lt x\lt5 .\end{array} The graph above confirms the solution set of the inequality.