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: 20

Answer

The solutions are $x=1$ and $x=0$

Work Step by Step

$|x+1|=|1-3x|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $x+1=1-3x$ and $x+1=-(1-3x)$ $\textbf{Solve the first equation:}$ $x+1=1-3x$ Take $3x$ to the left side and $1$ to the right side: $x+3x=1-1$ $4x=0$ Solve for $x$: $x=\dfrac{0}{4}$ $x=0$ $\textbf{Solve the second equation:}$ $x+1=-(1-3x)$ $x+1=-1+3x$ Take $3x$ to the left side and $1$ to the right side: $x-3x=-1-1$ $-2x=-2$ Solve for $x$: $x=\dfrac{-2}{-2}$ $x=1$ The solutions are $x=1$ and $x=0$
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