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