Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 4 - Proportions, Percents, and Solving Inequalities - 4.5 - Inequalities, Compound Inequalities, and Problem Solving - Problem Set 4.5 - Page 175: 31

Answer

$n\le42$

Work Step by Step

Multiplying both sides by the $LCD= 6 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{1}{2}n-\dfrac{2}{3}n\ge-7 ,$ is \begin{array}{l}\require{cancel} 3(1n)-2(2n)\ge6(-7) \\\\ 3n-4n\ge-42 \\\\ -n\ge-42 \\\\ n\le42 .\end{array}
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