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 - Page 168: 44


The solutions are $x=3$ and $x=\dfrac{7}{3}$

Work Step by Step

$|8-3x|-3=-2$ Take $3$ to the right side of the equation: $|8-3x|=-2+3$ $|8-3x|=1$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $8-3x=1$ and $8-3x=-1$ $\textbf{Solve the first equation:}$ $8-3x=1$ Take $8$ to the right side: $-3x=1-8$ $-3x=-7$ Solve for $x$: $x=\dfrac{-7}{-3}$ $x=\dfrac{7}{3}$ $\textbf{Solve the second equation:}$ $8-3x=-1$ Take $8$ to the right side: $-3x=-1-8$ $-3x=-9$ Solve for $x$: $x=\dfrac{-9}{-3}$ $x=3$ The solutions are $x=3$ and $x=\dfrac{7}{3}$
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