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: 35

Answer

a. $0$ b. $\{ 2 \}$

Work Step by Step

$\frac{2}{3x} + \frac{1}{4} = \frac{11}{6x} - \frac{1}{3}$ a. $x=0$, makes the denominator zero, it is the restricted value. b. $\frac{2}{3x} + \frac{1}{4} = \frac{11}{6x} - \frac{1}{3} ; x \ne 0;$ Multiply both sides, by the LCD $12x$. $12x(\frac{2}{3x} + \frac{1}{4}) = 12x(\frac{11}{6x} - \frac{1}{3}) ; x \ne 0;$ Using Distributive property, $12x(\frac{2}{3x}) + 12x(\frac{1}{4}) = 12x(\frac{11}{6x}) - 12x(\frac{1}{3}) ; x \ne 0;$ Divide out common factors. $8 + 3x = 22 - 4x$ $3x + 4x = 22 - 8$ $7x = 14$ $x = 2$ $2 $ is not the restricted value, Solution : $\{ 2 \}$
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