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 $x=-\dfrac{7}{3}$
