\(\dfrac{1}{2}+x+\dfrac{3}{2}.\left(x+1\right)=\dfrac{1}{3}\)
\(\dfrac{1}{2}+x+\dfrac{3}{2}.x+\dfrac{3}{2}=\dfrac{1}{3}\)
\(\left(x+\dfrac{3}{2}.x\right)+\left(\dfrac{1}{2}+\dfrac{3}{2}\right)=\dfrac{1}{3}\)
\(\dfrac{5}{2}.x+2=\dfrac{1}{3}\)
\(\dfrac{5}{2}.x=\dfrac{1}{3}-2\)
\(\dfrac{5}{2}.x=\dfrac{-5}{3}\)
\(x=\dfrac{-5}{3}:\dfrac{5}{2}\)
\(x=\dfrac{-2}{3}\)