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: 46

Answer

The solutions are $x=\dfrac{1}{2}$ and $x=\dfrac{3}{2}$

Work Step by Step

$|4-4x|+2=4$ Take $2$ to the right side of the equation: $|4-4x|=4-2$ $|4-4x|=2$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $4-4x=2$ and $4-4x=-2$ $\textbf{Solve the first equation:}$ $4-4x=2$ Take $4$ to the right side: $-4x=2-4$ $-4x=-2$ Solve for $x$: $x=\dfrac{-2}{-4}$ $x=\dfrac{1}{2}$ $\textbf{Solve the second equation:}$ $4-4x=-2$ Take $4$ to the right side: $-4x=-2-4$ $-4x=-6$ Solve for $x$: $x=\dfrac{-6}{-4}$ $x=\dfrac{3}{2}$ The solutions are $x=\dfrac{1}{2}$ and $x=\dfrac{3}{2}$
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