There are 4 cases :

+ \(x< -2\)

\(-x-2=1-3x\Leftrightarrow2x=3\Leftrightarrow x=\dfrac{3}{2}\) (asburd)

+ \(-2\le x< \dfrac{1}{3}\)

\(x+2=1-3x\Leftrightarrow4x=-1\Leftrightarrow x=-\dfrac{1}{4}\) (satisfied)

+ \(x\ge\dfrac{1}{3}\)

\(x+2=3x-1\Leftrightarrow3=2x\Leftrightarrow x=\dfrac{3}{2}\) (satisfied)

So, \(S=\left\{-\dfrac{1}{4};\dfrac{3}{2}\right\}\)