\(x-\frac{2x+1}{2}-\frac{x+2}{3}>11\)
\(\Leftrightarrow\frac{6x}{6}-\frac{3.\left(2x+1\right)}{6}-\frac{2.\left(x+2\right)}{6}>11\)
\(\Leftrightarrow\frac{6x-6x-3-2x-4}{6}>11\)
\(\Leftrightarrow\frac{-2x-7}{6}>11\)
\(\Leftrightarrow-2x-7>66\)
\(\Leftrightarrow-2x>73\)
\(\Leftrightarrow x< \frac{-73}{2}\)