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: 34

Answer

a. $0$ b. $\{ \frac{1}{4} \}$

Work Step by Step

$\frac{7}{2x} - \frac{5}{3x} = \frac{22}{3}$ a. $x=0$, makes the denominator zero, so it is the restricted value. b. $\frac{7}{2x} - \frac{5}{3x} = \frac{22}{3} ; x \ne 0;$ Multiply both sides, by the LCD $6x$. $6x(\frac{7}{2x} - \frac{5}{3x}) = 6x(\frac{22}{3}) ; x \ne 0;$ Using Distributive property, $6x(\frac{7}{2x}) - 6x( \frac{5}{3x}) = 6x(\frac{22}{3}) ; x \ne 0;$ Divide out common factors. $3(7) -2(5) = 2x(22)$ $21-10 = 44x$ $11 = 44x$ $x = \frac{11}{44}$ $x = \frac{1}{4}$ $\frac{1}{4} $ is not the restricted value. Solution Set : $\{\frac{1}{4} \}$
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