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: 19

Answer

The solutions are $x=-\dfrac{1}{7}$ and $x=-\dfrac{7}{3}$

Work Step by Step

$|2x-3|=|5x+4|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $2x-3=5x+4$ and $2x-3=-(5x+4)$ $\textbf{Solve the first equation:}$ $2x-3=5x+4$ Take $5x$ to the left side and $3$ to the right side: $2x-5x=4+3$ $-3x=7$ Solve for $x$: $x=-\dfrac{7}{3}$ $\textbf{Solve the second equation:}$ $2x-3=-(5x+4)$ $2x-3=-5x-4$ Take $5x$ to the left side and $3$ to the right side: $2x+5x=-4+3$ $7x=-1$ $x=-\dfrac{1}{7}$ The solutions are $x=-\dfrac{1}{7}$ and $x=-\dfrac{7}{3}$
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