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: 22

Answer

$(7,\infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ \dfrac{3x-1}{4}\gt5 ,$ 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} 4\cdot\dfrac{3x-1}{4}\gt4\cdot5 \\\\ 3x-1\gt20 \\\\ 3x\gt20+1 \\\\ 3x\gt21 \\\\ x\gt\dfrac{21}{3} \\\\ x\gt7 .\end{array} The red graph is the graph of the solution set. In interval notation, the solution set is $ (7,\infty) .$
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