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: 21

Answer

The solution is $x=1$

Work Step by Step

$|4-3x|=|2-3x|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $4-3x=2-3x$ and $4-3x=-(2-3x)$ $\textbf{Solve the first equation:}$ $4-3x=2-3x$ Take $3x$ to the left side and and $4$ to the right side: $-3x+3x=2-4$ $0\ne-2$ False This equation has no solution. $\textbf{Solve the second equation:}$ $4-3x=-(2-3x)$ $4-3x=-2+3x$ Take $3x$ to the left side and and $4$ to the right side: $-3x-3x=-2-4$ $-6x=-6$ Solve for $x$: $x=\dfrac{-6}{-6}$ $x=1$ The solution is $x=1$
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