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 - Review Exercises: Chapter 2: 47

Answer

$\text{Set Builder Notation: } \left\{ x|x\le-8 \right\} \\\text{Interval Notation: } \left( -\infty,-8 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ 7\le1-\dfrac{3}{4}x .$ 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} 7\le1-\dfrac{3}{4}x \\\\ 4(7)\le4\left( 1-\dfrac{3}{4}x \right) \\\\ 28\le4-3x \\\\ 3x\le4-28 \\\\ 3x\le-24 \\\\ x\le-\dfrac{24}{3} \\\\ x\le-8 .\end{array} Hence, the solution set is \begin{array}{l}\require{cancel} \text{Set Builder Notation: } \left\{ x|x\le-8 \right\} \\\text{Interval Notation: } \left( -\infty,-8 \right] .\end{array}
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