\(\dfrac{\left(2x+1\right)}{2}-\dfrac{1}{3}=\dfrac{\left(x+1\right)}{6}\left(MC=12\right)\\ \Leftrightarrow\dfrac{\left(2x+1\right)2}{2.6}-\dfrac{1.4}{3.4}=\dfrac{\left(x+1\right)2}{6.2}\\ \Leftrightarrow\dfrac{4x+2}{12}-\dfrac{4}{12}=\dfrac{2x+2}{12}\\ \Leftrightarrow4x+2-4=2x+2\\ \Leftrightarrow4x-2x=2+2-4\\ \Leftrightarrow2x=0\\ \Leftrightarrow x=0\)