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: 43

Answer

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

Work Step by Step

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