Answer
The solutions are $x=\dfrac{2}{9}$ and $x=-\dfrac{4}{3}$
Work Step by Step
$\Big|\dfrac{6x+1}{x-1}\Big|=3$
Solving this absolute value equation is equivalent to solving two equations, which are:
$\dfrac{6x+1}{x-1}=3$ and $\dfrac{6x+1}{x-1}=-3$
Solve the first equation:
$\dfrac{6x+1}{x-1}=3$
Take $x-1$ to multiply the right side:
$6x+1=3(x-1)$
$6x+1=3x-3$
Take $3x$ to the left side and $1$ to the right side:
$6x-3x=-3-1$
$3x=-4$
Solve for $x$:
$x=-\dfrac{4}{3}$
Solve the second equation:
$\dfrac{6x+1}{x-1}=-3$
Take $x-1$ to multiply the right side:
$6x+1=-3(x-1)$
$6x+1=-3x+3$
Take $3x$ to the left side and $1$ to the right side:
$6x+3x=3-1$
$9x=2$
Solve for $x$:
$x=\dfrac{2}{9}$
The solutions are $x=\dfrac{2}{9}$ and $x=-\dfrac{4}{3}$
