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: 22


$\text{Set Builder Notation: } \left\{ t|t\le-2 \right\} \\\text{Interval Notation: } \left( -\infty,-2 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 4t+10\le2 .$ 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} 4t+10\le2 \\\\ 4t\le2-10 \\\\ 4t\le-8 \\\\ t\le-\dfrac{8}{4} \\\\ t\le-2 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ t|t\le-2 \right\} \\\text{Interval Notation: } \left( -\infty,-2 \right] .\end{array}
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