Chapter 2 - Equations, Inequalities, and Problem Solving - Test: Chapter 2 - Page 151: 17

$\text{Set Builder Notation: } \left\{ x|x\le-1 \right\} \\\text{Interval Notation: } \left( -\infty,-1 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $5-9x\ge19+5x .$ 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} 5-9x\ge19+5x \\\\ -9x-5x\ge19-5 \\\\ -14x\ge14 .\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} -14x\ge14 \\\\ x\le\dfrac{14}{-14} \\\\ x\le-1 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ x|x\le-1 \right\} \\\text{Interval Notation: } \left( -\infty,-1 \right] .\end{array}

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