`a)`\(\dfrac{3x-5}{7}< x-2< \dfrac{x+7}{11}\)
\(\Leftrightarrow\dfrac{11\left(3x-5\right)}{77}< \dfrac{77\left(x-2\right)}{77}< \dfrac{7\left(x+7\right)}{77}\)
\(\Leftrightarrow11\left(3x-5\right)< 77\left(x-2\right)< 7\left(x+7\right)\)
\(\Leftrightarrow33x-55< 77x-154< 7x+49\)
\(\Leftrightarrow-51x< 258\)
\(\Leftrightarrow x>-\dfrac{86}{17}\)
Vậy \(S=\left\{x|x>=\dfrac{86}{17}\right\}\)
`b)`\(\dfrac{-6x-3}{2}\le\dfrac{x+3}{3}\le x-4\)
\(\Leftrightarrow\dfrac{3\left(-6x-3\right)}{6}\le\dfrac{2\left(x+3\right)}{6}\le\dfrac{6\left(x-4\right)}{6}\)
\(\Leftrightarrow3\left(-6x-3\right)\le2\left(x+3\right)\le6\left(x-4\right)\)
\(\Leftrightarrow-18x-9\le2x+6\le6x-24\)
\(\Leftrightarrow-26x\le-21\)
\(\Leftrightarrow x\ge\dfrac{21}{26}\)
Vậy \(S=\left\{x|x\ge\dfrac{21}{26}\right\}\)