To solve the equation \( \frac{5}{2}x = -\frac{1}{8} \), we can start by isolating \( x \).
- Multiply 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, compute the right-hand side:
\[ x = -\frac{1 \cdot 2}{8 \cdot 5} = -\frac{2}{40} \]
- Simplify \( -\frac{2}{40} \):
\[ -\frac{2}{40} = -\frac{1}{20} \]
Thus, the solution to the equation is
\[ \boxed{-\frac{1}{20}} \]