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: 21

Answer

$(-\infty,14)$
1512736810

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ \dfrac{5x-6}{8}\lt8 ,$ use 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 properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 8\cdot\dfrac{5x-6}{8}\lt8\cdot8 \\\\ 5x-6\lt64 \\\\ 5x\lt64+6 \\\\ 5x\lt70 \\\\ x\lt\dfrac{70}{5} \\\\ x\lt14 .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ (-\infty,14) .$
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