To solve the equation \(\frac{1}{5} - \frac{1}{2} = \frac{3}{x}\), we need to find a common denominator for the fractions on the left side.
The least common multiple of 5 and 2 is 10. So we can rewrite the fractions:
\[ \frac{1}{5} = \frac{2}{10} \] \[ \frac{1}{2} = \frac{5}{10} \]
Now, substituting those values into the equation, we get:
\[ \frac{2}{10} - \frac{5}{10} = \frac{3}{x} \]
Subtracting the left side:
\[ \frac{2 - 5}{10} = \frac{3}{x} \] \[ \frac{-3}{10} = \frac{3}{x} \]
Next, cross-multiply to solve for \(x\):
\[ -3x = 30 \]
Now, divide both sides by -3:
\[ x = -10 \]
So, the solution is:
\[ \boxed{-10} \]