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 1-2 - Cumulative Review - Page 152: 24


$\text{Set Builder Notation: } \left\{ x|x\lt30 \right\} \\\text{Interval Notation: } \left( -\infty,30 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 4\lt10-\dfrac{x}{5} .$ 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} 4\lt10-\dfrac{x}{5} \\\\ \dfrac{x}{5}\lt10-4 \\\\ \dfrac{x}{5}\lt6 \\\\ 5\left( \dfrac{x}{5} \right) \lt5(6) \\\\ x\lt30 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ x|x\lt30 \right\} \\\text{Interval Notation: } \left( -\infty,30 \right) .\end{array}
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