\(\frac{1}{2}-\frac{1}{3}+\left(\frac{1}{2}x-\frac{1}{3}\right)=\frac{5}{6}\)
\(\frac{1}{6}+\left(\frac{1}{2}x-\frac{1}{3}\right)=\frac{5}{6}\)
\(\frac{1}{2}x-\frac{1}{3}=\frac{5}{6}-\frac{1}{6}\)
\(\frac{1}{2}x-\frac{1}{3}=\frac{2}{3}\)
\(\frac{1}{2}x=\frac{2}{3}+\frac{1}{3}\)
\(\frac{1}{2}x=1\)
\(x=2\)