# Chapter 2 - Equations, Inequalities, and Problem Solving - Test: Chapter 2: 15

$\text{Set Builder Notation: } \left\{ x|x\lt-7 \right\} \\\text{Interval Notation: } \left( -\infty,-7 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $3-5x\gt38 .$ Write the answer in both set-builder notation and interval notation. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 3-5x\gt38 \\\\ -5x\gt38-3 \\\\ -5x\gt35 .\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} -5x\gt35 \\\\ x\lt\dfrac{35}{-5} \\\\ x\lt-7 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ x|x\lt-7 \right\} \\\text{Interval Notation: } \left( -\infty,-7 \right) .\end{array}

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