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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.6 Solving Inequalities - 2.6 Exercise Set - Page 135: 65


$\text{Set Builder Notation: } \{ y|y\ge-\dfrac{1}{10} \} \\\text{Interval Notation: } \left[ -\dfrac{1}{10},\infty \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -2y\le\dfrac{1}{5} .$ 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 $\ge.$ $\bf{\text{Solution Details:}}$ Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -2y\le\dfrac{1}{5} \\\\ y\ge\dfrac{\dfrac{1}{5}}{-2} \\\\ y\ge\dfrac{1}{5}\div-2 \\\\ y\ge\dfrac{1}{5}\cdot\left(-\dfrac{1}{2} \right) \\\\ y\ge-\dfrac{1}{10} .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \{ y|y\ge-\dfrac{1}{10} \} \\\text{Interval Notation: } \left[ -\dfrac{1}{10},\infty \right) .\end{array}
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