Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.5 - Linear Inequalities in One Variable - 1.5 Exercises: 35

Answer

$\left( -\infty,\dfrac{76}{11} \right)$
1512799940

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ -\dfrac{1}{4}(p+6)+\dfrac{3}{2}(2p-5)\lt10 ,$ use the Distributive Property and the properties of inequality. For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$ For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$ $\bf{\text{Solution Details:}}$ Using the Distributive Property and the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 4\left(-\dfrac{1}{4}(p+6)+\dfrac{3}{2}(2p-5)\right)\lt4(10) \\\\ -1(p+6)+6(2p-5)\lt40 \\\\ -p-6+12p-30\lt40 \\\\ -p+12p\lt40+6+30 \\\\ 11p\lt76 \\\\ p\lt\dfrac{76}{11} .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ \left( -\infty,\dfrac{76}{11} \right) .$
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