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 - Page 100: 36


$\left( -\infty,\dfrac{49}{2} \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ \dfrac{3}{5}(t-2)-\dfrac{1}{4}(2t-7)\le3 ,$ 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} 20\left( \dfrac{3}{5}(t-2)-\dfrac{1}{4}(2t-7)\right)\le20(3) \\\\ 12(t-2)-5(2t-7)\le60 \\\\ 12(t)+12(-2)-5(2t)-5(-7)\le60 \\\\ 12t-24-10t+35\le60 \\\\ 12t-10t\le60+24-35 \\\\ 2t\le49 \\\\ t\le\dfrac{49}{2} .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ \left( -\infty,\dfrac{49}{2} \right] .$
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