Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 62


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

Work Step by Step

$\frac{x-4}{2x+1}$ $\lt$ 5 $\frac{x-4}{2x+1}$ -$\frac{5(2x+1)}{2x+1}$ $\lt$ 0 $\frac{-9x-9}{2x+1}$ $\lt$ 0 Factors are zero when x=-1 or x=-$\frac{1}{2}$, we can't include -$\frac{1}{2}$ in the solution because the denominator can't be zero (endpoints don't satisfy the inequality anyway) , these two points divide the number line into three intervals, plug in the value from each interval to decide which intervals are the solution.
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