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 - Test: Chapter 2 - Page 151: 14


$\text{Set Builder Notation: } \left\{ n|n\lt-5 \right\} \\\text{Interval Notation: } \left( -\infty,-5 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 4n+3\lt-17 .$ 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} 4n+3\lt-17 \\\\ 4n\lt-17-3 \\\\ 4n\lt-20 \\\\ n\lt-\dfrac{20}{4} \\\\ n\lt-5 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ n|n\lt-5 \right\} \\\text{Interval Notation: } \left( -\infty,-5 \right) .\end{array}
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