To solve the equation \( \frac{5}{8}(x - \frac{1}{2}) = 10 \), the first step to eliminate the fraction is to multiply both sides by the reciprocal of \( \frac{5}{8} \), which is \( \frac{8}{5} \).
However, to answer your question on what number you should divide both sides by in order to reverse the multiplication by \( \frac{5}{8} \), you would actually need to divide both sides by \( \frac{5}{8} \).
Dividing by \( \frac{5}{8} \) is equivalent to multiplying by its reciprocal \( \frac{8}{5} \).
Thus, to reverse the multiplication by \( \frac{5}{8} \), you should divide both sides of the equation by \( \frac{5}{8} \) to simplify it to:
\[ x - \frac{1}{2} = 10 \cdot \frac{8}{5} \]
This will help you isolate \( x \) in subsequent steps.
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