## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 135: 45

#### Answer

$\text{Set Builder Notation: } \{y|y\gt3\} \\\text{Interval Notation: } (3,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $y+6\gt9 .$ 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 is equivalent to \begin{array}{l}\require{cancel} y+6\gt9 \\\\ y\gt9-6 \\\\ y\gt3 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{y|y\gt3\} \\\text{Interval Notation: } (3,\infty) .\end{array}

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