\(\dfrac{1}{2}x-\dfrac{2}{3}\left(x+1\right)=-\dfrac{1}{12}\)
=>\(\dfrac{1}{2}x-\dfrac{2}{3}x-\dfrac{2}{3}=-\dfrac{1}{12}\)
=>\(\dfrac{-1}{6}x=-\dfrac{1}{12}+\dfrac{2}{3}=-\dfrac{1}{12}+\dfrac{8}{12}=\dfrac{7}{12}\)
=>\(x=\dfrac{7}{12}\cdot\left(-6\right)=-\dfrac{7}{2}\)