\(2\left(x-\frac{1}{2}\right)+3\left(-1+\frac{x}{3}\right)=x\left(\frac{2}{x}-1\right)\)
\(\Leftrightarrow2x-1-3+\frac{3x}{3}=\frac{2x}{x}-x\)
\(\Leftrightarrow2x-1-3+x=x-x\)
\(\Leftrightarrow2x-4+x=0\)
\(\Leftrightarrow3x-4=0\)
\(\Leftrightarrow3x=0+4\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=\frac{4}{3}\)