# Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set - Page 599: 59

$t\lt0 \text{ or } t\gt0$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Solve the given inequality, $|t|\gt0 ,$ using the definition of a greater than absolute value inequality. Then graph the solution set. 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 $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the given inequality is equivalent to \begin{array}{l}\require{cancel} t\gt0 \\\\\text{OR}\\\\ t\lt0 .\end{array} Hence, the solution set is $t\lt0 \text{ or } t\gt0 .$

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