\(\dfrac{1}{2}\cdot x+\dfrac{3}{5}\cdot\left(x-2\right)=3\\ \dfrac{1}{2}x+\dfrac{3}{5}x-\dfrac{3}{5}\cdot2=3\\ x\cdot\left(\dfrac{1}{2}+\dfrac{3}{5}\right)-\dfrac{6}{5}=3\\ \dfrac{11}{10}x=3+\dfrac{6}{5}\\ \dfrac{11}{10}x=\dfrac{21}{5}\\ x=\dfrac{21}{5}:\dfrac{11}{10}\\ x=\dfrac{42}{11}\)