\(3=\frac{1}{2}\times x+\frac{3}{5}\left(x-2\right)\)
\(3=\frac{1}{2}\times x+\frac{3}{5}\times x-\frac{3}{5}\times2\)
\(3+\frac{6}{5}=x\left(\frac{1}{2}+\frac{3}{5}\right)\)
\(\frac{21}{5}=x\times\frac{11}{10}\)
\(x=\frac{21}{5}:\frac{11}{10}=\frac{21}{5}\times\frac{10}{11}\)
\(x=\frac{42}{11}\)