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: 45

Answer

$x\gt64$

Work Step by Step

Multiplying both sides by the $LCD= 30 $ and then using the properties of inequalities, the solution to the given inequality, $ \dfrac{x+2}{6}-\dfrac{x+1}{5}\lt-2 ,$ is \begin{array}{l}\require{cancel} 5(x+2)-6(x+1)\lt30(-2) \\\\ 5x+10-6x-6\lt-60 \\\\ 5x-6x\lt-60-10+6 \\\\ -x\lt-64 \\\\ x\gt64 .\end{array}
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