\(\dfrac{1}{11}\left(1-3x\right)=\dfrac{1}{5}x-\dfrac{1}{2}\\ \Leftrightarrow\dfrac{1}{11}-\dfrac{3}{11}x=\dfrac{1}{5}x-\dfrac{1}{2}\\ \Leftrightarrow\dfrac{1}{5}x-\dfrac{1}{2}+\dfrac{1}{11}+\dfrac{3}{11}x=0\\ \Leftrightarrow\dfrac{26}{55}x-\dfrac{9}{22}=0\\ \Leftrightarrow\dfrac{26}{55}x=\dfrac{9}{22}\\ \Leftrightarrow x=\dfrac{45}{52}\)