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

\(\Leftrightarrow\dfrac{6x-2\left(x+\dfrac{1}{2}\right)+6}{6}=\dfrac{3\left(x+\dfrac{1}{3}\right)}{6}\)

\(\Leftrightarrow6x-2x-1+6=3x+1\)

\(\Leftrightarrow6x-2x-3x=1+1-6\Leftrightarrow x=-4\)