College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.8 - Solving Absolute Value Equations and Inequalities - 1.8 Exercises: 43

Answer

Interval: $(- \infty,\ -\frac{1}{2})\cup\ (\frac{1}{3},\ \infty)$

Work Step by Step

$\frac{1}{2}|4x+\frac{1}{3}|\gt\frac{5}{6}$ $|4x+\frac{1}{3}|\gt\frac{5*2}{6}$ $|4x+\frac{1}{3}|\gt\frac{5}{3}$ We split the absolute value into the positive and negative: $4x+ \frac{1}{3}\gt\frac{5}{3}$ $ 4x\gt\frac{4}{3}$ $ x\gt\frac{1}{3}$ $4x+ \frac{1}{3}\lt-\frac{5}{3}$ $4x\lt-\frac{5}{3}-\frac{1}{3}$ $4x\lt-2$ $x\lt-\frac{1}{2}$ Interval: $(- \infty,\ -\frac{1}{2})\cup\ (\frac{1}{3},\ \infty)$
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