Chapter 2 - Equations, Inequalities, and Problem Solving - Review Exercises: Chapter 2 - Page 149: 43

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $-4y\lt28 .$ Write the answer in both set-builder notation and interval notation. $\bf{\text{Solution Details:}}$ Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -4y\lt28 \\\\ y\gt\dfrac{28}{-4} \\\\ y\gt-7 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ y|y\gt-7 \right\} \\\text{Interval Notation: } \left( -7,\infty \right) .\end{array}

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