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: 45


The solutions are $x=2$ and $x=4$

Work Step by Step

$|6-2x|+1=3$ Take $1$ to the right side of the equation: $|6-2x|=3-1$ $|6-2x|=2$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $6-2x=2$ and $6-2x=-2$ $\textbf{Solve the first equation:}$ $6-2x=2$ Take $6$ to the right side: $-2x=2-6$ $-2x=-4$ Solve for $x$: $x=\dfrac{-4}{-2}$ $x=2$ $\textbf{Solve the second equation:}$ $6-2x=-2$ Take $6$ to the right side: $-2x=-2-6$ $-2x=-8$ Solve for $x$: $x=\dfrac{-8}{-2}$ $x=4$ The solutions are $x=2$ and $x=4$
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