Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises: 18

Answer

The solutions are $x=7$ and $x=\dfrac{1}{5}$

Work Step by Step

$\Big|\dfrac{2x+3}{3x-4}\Big|=1$ Solving this absolute value equation is equivalent to solving two equations, which are: $\dfrac{2x+3}{3x-4}=1$ and $\dfrac{2x+3}{3x-4}=-1$ Solve the first equation: $\dfrac{2x+3}{3x-4}=1$ Take $3x-4$ to multiply the right side: $2x+3=3x-4$ Take $3x$ to the left side and $3$ to the right side: $2x-3x=-4-3$ $-x=-7$ Solve for $x$: $x=7$ Solve the second equation: $\dfrac{2x+3}{3x-4}=-1$ Take $3x-4$ to multiply the right side: $2x+3=-3x+4$ Take $3x$ to the left side and $3$ to the right side: $2x+3x=4-3$ $5x=1$ Solve for $x$: $x=\dfrac{1}{5}$ The solutions are $x=7$ and $x=\dfrac{1}{5}$
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