a) \(\dfrac{2x-1}{3}< \dfrac{x+6}{2}\)
\(\Leftrightarrow2\left(2x-1\right)< 3\left(x+6\right)\)
\(\Leftrightarrow4x-2< 3x+18\)
\(\Leftrightarrow x< 20\)
b) \(\dfrac{5\left(x-1\right)}{6}-1\ge\dfrac{2\left(x+1\right)}{3}\)
\(\Leftrightarrow5\left(x-1\right)-6\ge2.2\left(x+1\right)\)
\(\Leftrightarrow5x-5-6\ge4x+2\)
\(\Leftrightarrow x\ge13\)