$\begin{array} { l }|\frac{ 3 }{ x-2 }|=\frac{ 1 }{ 2 },& x≠2\end{array}$
Use $|\frac{ a }{ b }|=\frac{ |a| }{ |b| }$ to transform the expression$\frac{ |3| }{ |x-2| }=\frac{ 1 }{ 2 }$
The absolute value of any number is always positive$\frac{ 3 }{ |x-2| }=\frac{ 1 }{ 2 }$
Simplify the equation using cross-multiplication$6=|x-2|$
Swap the sides of the equation$|x-2|=6$
Use the absolute value definition to rewrite the absolute value equation as two separate equations$\begin{array} { l }x-2=6,\\x-2=-6\end{array}$
Solve the equation for $x$$\begin{array} { l }x=8,\\x-2=-6\end{array}$
Solve the equation for $x$$\begin{array} { l }\begin{array} { l }x=8,\\x=-4\end{array},& x≠2\end{array}$
Check if the solution is in the defined range$\begin{array} { l }x=8,\\x=-4\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-4,& x_2=8\end{array}$