Solution:

For above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0.

\[\begin{array}{*{35}{l}}

\Rightarrow ~6\text{ }\text{ }-33x\text{ }>\text{ }0\text{ }and\text{ }7x\text{ }\text{ }-1\text{ }>\text{ }0  \\

\Rightarrow ~33x\text{ }<\text{ }6\text{ }and\text{ }7x\text{ }>\text{ }1  \\

\Rightarrow ~x\text{ }<\text{ }2/11\text{ }and\text{ }x\text{ }>\text{ }1/7  \\

\Rightarrow ~1/7\text{ }<\text{ }x\text{ }<\text{ }2/11\text{ }\ldots \left( i \right)  \\

Or  \\

\Rightarrow ~6\text{ }\text{ }-33x\text{ }<\text{ }0\text{ }and\text{ }7x\text{ }\text{ }-1\text{ }<\text{ }0  \\

\Rightarrow ~33x\text{ }>\text{ }6\text{ }and\text{ }7x\text{ }<\text{ }1  \\

\Rightarrow ~x\text{ }>\text{ }2/11\text{ }and\text{ }x\text{ }<\text{ }1/7  \\

\Rightarrow ~2/11<\text{ }x\text{ }<\text{ }1/7\text{ }\ldots   \\

\end{array}\](which is not possible since 1/7 > 2/11)

Also,

For above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0.

\[\begin{array}{*{35}{l}}

\Rightarrow ~23\text{ }\text{ }-x\text{ }>\text{ }0\text{ }and\text{ }x\text{ }\text{ }-8\text{ }>\text{ }0  \\

\Rightarrow ~x\text{ }<\text{ }23\text{ }and\text{ }x\text{ }>\text{ }8  \\

\Rightarrow ~8\text{ }<\text{ }x\text{ }<\text{ }23\text{ }\ldots \left( ii \right)  \\

Or  \\

23\text{ }\text{ }-x\text{ }<\text{ }0\text{ }and\text{ }x\text{ }\text{ }-8\text{ }<\text{ }0  \\

\Rightarrow ~x\text{ }>\text{ }23\text{ }and\text{ }x\text{ }<\text{ }8  \\

\Rightarrow ~23\text{ }<\text{ }x\text{ }<\text{ }8\text{ }\ldots   \\

\end{array}\]

(which is not possible, as 23 > 8]

Therefore, from equations (i) and (ii), we infer that there is no solution satisfying both inequalities.

Hence, the given system has no solution.