\[\begin{array}{*{35}{l}}
4x\text{ }+\text{ }3\text{ }\ge \text{ }2x\text{ }+\text{ }17 \\
\Rightarrow ~4x\text{ }\text{ }-2x\text{ }\ge \text{ }17\text{ }\text{ }-3 \\
\Rightarrow ~2x\text{ }\ge \text{ }14 \\
\Rightarrow ~x\text{ }\ge \text{ }7\text{ }\ldots \left( i \right) \\
Also, \\
3x\text{ }\text{ }-5\text{ }<\text{ }\text{ }2 \\
\Rightarrow ~3x\text{ }<\text{ }3 \\
\Rightarrow ~x\text{ }<\text{ }1\text{ }\ldots \left( 2 \right) \\
\end{array}\]
Since, equations [i] and [ii] cannot be possible simultaneously,
We conclude that x has no solution.