\(2\left(x+1\right)-3\left(2x+1\right)\ne0\\ \Leftrightarrow2x+2-6x-3\ne0\\ \Leftrightarrow-4x-1\ne0\\ \Leftrightarrow-4x\ne1\\ \Leftrightarrow x\ne\dfrac{-1}{4}\)
\(\dfrac{x+1}{2}-3=2x-\dfrac{1}{3}\\ \Leftrightarrow\dfrac{3\left(x+1\right)}{6}-\dfrac{18}{6}=\dfrac{12x}{6}-\dfrac{2}{6}\\ \Leftrightarrow3\left(x+1\right)-18=12x-2\\ \Leftrightarrow3x+3-18-12x+2=0\\ \Leftrightarrow-9x-13=0\\ \Leftrightarrow-9x=13\\ \Leftrightarrow x=-\dfrac{13}{9}\)





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