To solve the equation \(\frac{5}{2}x = -\frac{1}{8}\), we need to isolate \(x\).
- Start by multiplying both sides of the equation by the reciprocal of \(\frac{5}{2}\), which is \(\frac{2}{5}\):
\[ x = -\frac{1}{8} \cdot \frac{2}{5} \]
- Now perform the multiplication on the right side:
\[ x = -\frac{1 \cdot 2}{8 \cdot 5} = -\frac{2}{40} \]
- Simplify \(-\frac{2}{40}\):
\[ x = -\frac{1}{20} \]
Thus, the solution to the equation \(\frac{5}{2}x = -\frac{1}{8}\) is:
\[ \boxed{-\frac{1}{20}} \]
The correct response is \(-\frac{1}{20}\) (negative Start Fraction 1 over 20 End Fraction).