\(\frac{2}{3}x-\frac{3}{2}\left(x-\frac{1}{2}\right)=\frac{5}{12}\)
\(\Rightarrow\frac{2}{3}x-\frac{3}{2}x+\frac{3}{4}=\frac{5}{12}\)
\(\Rightarrow\left(\frac{2}{3}-\frac{3}{2}\right)x=\frac{5}{12}-\frac{3}{4}\)
\(\Rightarrow-\frac{5}{6}x=-\frac{1}{3}\)
\(\Rightarrow x=\left(-\frac{1}{3}\right):\left(-\frac{5}{6}\right)\)
\(\Rightarrow x=\frac{2}{5}\)