#### Answer

The solutions are $x=\dfrac{7}{8}$ and $x=\dfrac{1}{8}$

#### Work Step by Step

$\Big|\dfrac{3}{2x-1}\Big|=4$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$\dfrac{3}{2x-1}=4$ and $\dfrac{3}{2x-1}=-4$
Solve the first equation:
$\dfrac{3}{2x-1}=4$
Take $2x-1$ to multiply the right side:
$3=4(2x-1)$
$3=8x-4$
Solve for $x$:
$-8x=-4-3$
$-8x=-7$
$x=\dfrac{-7}{-8}$
$x=\dfrac{7}{8}$
Solve the second equation:
$\dfrac{3}{2x-1}=-4$
Take $2x-1$ to multiply the right side:
$3=-4(2x-1)$
$3=-8x+4$
Solve for $x$:
$8x=4-3$
$8x=1$
$x=\dfrac{1}{8}$
The solutions are $x=\dfrac{7}{8}$ and $x=\dfrac{1}{8}$