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: 93

Answer

$r\gt-3$

Work Step by Step

Remember that when we divide or multiply an inequality by a negative, we have to flip the sign of the inequality. Using the Distributive Property and the properties of inequality, the solution to the given inequality, $ 3(r-6)+2\lt4(r+2)-21 ,$ is \begin{array}{l}\require{cancel} 3(r)+3(-6)+2\lt4(r)+4(2)-21 \\\\ 3r-18+2\lt4r+8-21 \\\\ 3r-16\lt4r-13 \\\\ 3r-4r\lt-13+16 \\\\ -r\lt3 \\\\ r\gt-3 .\end{array}
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