# Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 135: 61

$\text{Set Builder Notation: } \{ t|t\lt-3 \} \\\text{Interval Notation: } (-\infty,-3)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-24\gt8t .$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set. In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality, the given equation is equivalent to \begin{array}{l}\require{cancel} -24\gt8t \\\\ -8t\gt24 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -8t\gt24 \\\\ t\lt\dfrac{24}{-8} \\\\ t\lt-3 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{ t|t\lt-3 \} \\\text{Interval Notation: } (-\infty,-3) .\end{array}

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