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: 16

Answer

The solutions are $x=\dfrac{7}{8}$ and $x=\dfrac{1}{8}$

Work Step by Step

$\Big|\dfrac{3}{2x-1}\Big|=4$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $\dfrac{3}{2x-1}=4$ and $\dfrac{3}{2x-1}=-4$ Solve the first equation: $\dfrac{3}{2x-1}=4$ Take $2x-1$ to multiply the right side: $3=4(2x-1)$ $3=8x-4$ Solve for $x$: $-8x=-4-3$ $-8x=-7$ $x=\dfrac{-7}{-8}$ $x=\dfrac{7}{8}$ Solve the second equation: $\dfrac{3}{2x-1}=-4$ Take $2x-1$ to multiply the right side: $3=-4(2x-1)$ $3=-8x+4$ Solve for $x$: $8x=4-3$ $8x=1$ $x=\dfrac{1}{8}$ The solutions are $x=\dfrac{7}{8}$ and $x=\dfrac{1}{8}$
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