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: 48

Answer

$n\lt\dfrac{68}{7}$

Work Step by Step

Multiplying both sides by the $LCD= 12 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{n-4}{4}+\dfrac{n-2}{3}\lt4 ,$ is \begin{array}{l}\require{cancel} 3(n-4)+4(n-2)\lt12(4) \\\\ 3n-12+4n-8\lt48 \\\\ 3n+4n\lt48+12+8 \\\\ 7n\lt68 \\\\ n\lt\dfrac{68}{7} .\end{array}
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