To solve the equation \( \frac{5}{2}x = -\frac{1}{8} \), we can isolate \( x \) by performing the following steps:
- Multiply both sides by the reciprocal of \( \frac{5}{2} \), which is \( \frac{2}{5} \):
\[ x = -\frac{1}{8} \times \frac{2}{5} \]
- Now perform the multiplication:
\[ x = -\frac{2}{40} \]
- Simplify \( -\frac{2}{40} \):
\[ x = -\frac{1}{20} \]
Now, let's compare this result to the given options:
-20
-1.20
1/20
-6/16
The correct answer is \(-\frac{1}{20}\), which can also be represented as -0.05 numerically. Therefore, the solution to the equation is:
\[ \boxed{-\frac{1}{20}} \]
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