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: 68

Answer

$\text{Set Builder Notation: } \left\{ y|y\lt\dfrac{1}{16} \right\} \\\text{Interval Notation: } \left(-\infty,\dfrac{1}{16} \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -\dfrac{5}{8}\lt-10y .$ 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} -\dfrac{5}{8}\lt-10y \\\\ 10y\lt\dfrac{5}{8} \\\\ y\lt\dfrac{\dfrac{5}{8}}{10} \\\\ y\lt\dfrac{5}{8}\div10 \\\\ y\lt\dfrac{5}{8}\cdot\dfrac{1}{10} \\\\ y\lt\dfrac{\cancel5}{8}\cdot\dfrac{1}{\cancel5(2)} \\\\ y\lt\dfrac{1}{16} .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ y|y\lt\dfrac{1}{16} \right\} \\\text{Interval Notation: } \left(-\infty,\dfrac{1}{16} \right) .\end{array}
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