College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.2 - Page 118: 38

Answer

a. 0 b. $\{ 8 \}$

Work Step by Step

$\frac{4}{x}= \frac{9}{5} - \frac{7x-4}{5x}$ a. $x =0 $ makes the denominator zero. So, $ x = 0$ is the restricted value. b. $\frac{4}{x}= \frac{9}{5} - \frac{7x-4}{5x}; x \ne 0;$ Take LCD at right hand side. $\frac{4}{x}= \frac{9x-(7x-4)}{5x}; x \ne 0;$ $\frac{4}{x}= \frac{9x-7x+4}{5x}; x \ne 0;$ $\frac{4}{x}= \frac{2x+4}{5x}; x \ne 0;$ Multiply both sides by $5x$. $5x(\frac{4}{x})= 5x(\frac{2x+4}{5x}); x \ne 0;$ $20 = 2x+4$ $20-4 = 2x$ $2x = 16$ $x = 8$ $8$ is not the restricted value. Solution set $:\{8 \}$
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