Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Review - Page 829: 30

Answer

$-5$

Work Step by Step

We put this word problem into an equation then simplify as follows: $x-\frac{1}{x}=-\frac{24}{5}$ $x(5x)-\frac{5x}{x}=-\frac{24(5x)}{5}$ $5x^{2}-5=-24x$ $5x^{2}+24x-5=0$ $(5x-1)(x+5)=0$ $5x-1=0$ or $x+5=0$ $5x=1$ or $x=-5$ $x=\frac{1}{5}$ or $x=-5$ We are told that the number is negative, so the only possible answer is $-5$
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