To solve the equation \( \frac{5}{2} x = -\frac{1}{8} \), we can isolate \( x \) by multiplying both sides of the equation by the reciprocal of \( \frac{5}{2} \), which is \( \frac{2}{5} \).
Here's how to solve it step by step:
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Start with the equation: \[ \frac{5}{2} x = -\frac{1}{8} \]
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Multiply both sides by \( \frac{2}{5} \): \[ x = -\frac{1}{8} \cdot \frac{2}{5} \]
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Perform the multiplication on the right side: \[ x = -\frac{1 \cdot 2}{8 \cdot 5} = -\frac{2}{40} = -\frac{1}{20} \]
Thus, the solution to the equation is: \[ \boxed{-\frac{1}{20}} \]
So the answer is \( -\frac{1}{20} \).