\(\frac{1}{2}x+\frac{7}{6}=\frac{9}{5}x-\frac{4}{3}\)
\(\Rightarrow\frac{9}{5}x-\frac{1}{2}x=\frac{7}{6}+\frac{4}{3}\)
\(x.\left(\frac{18}{10}-\frac{5}{10}\right)=\frac{7}{6}+\frac{8}{6}\)
\(\frac{13}{10}.x=\frac{15}{6}\)
\(\Rightarrow x=\frac{15}{6}:\frac{13}{10}\)
\(x=\frac{15}{6}.\frac{10}{13}\)
\(x=\frac{25}{13}\)