Answer 1

\[\frac{x}{x - 5} > \frac{1}{2}\]
\[ \Rightarrow \frac{x}{x - 5} - \frac{1}{2} > 0\]
\[ \Rightarrow \frac{2x - x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{x - 5} > 0\]  

\[\therefore x \in \left( - \infty , - 5 \right) \cup \left( 5, \infty \right)\]