\(2.\left(x+1\right)-\frac{1}{3}\left(x-1\right)=\frac{2}{3}\)
=> \(2x+1-\frac{1}{3}x+\frac{1}{3}=\frac{2}{3}\)
=> \(\left(2x-\frac{1}{3}x\right)+\left(1+\frac{1}{3}\right)=\frac{2}{3}\)
=> \(\frac{5}{3}x+\frac{4}{3}=\frac{2}{3}\)
=> \(\frac{5}{3}x=\frac{-2}{3}=>x=\frac{-5}{2}\)