To solve the equation \( \frac{5}{8}(x - \frac{1}{2}) = 10 \), the first step involves eliminating the fraction. Specifically, we want to reverse the multiplication by \( \frac{5}{8} \).
To do this, we should multiply both sides of the equation by the reciprocal of \( \frac{5}{8} \), which is \( \frac{8}{5} \).
So instead of dividing both sides by a number, you would multiply both sides by \( \frac{8}{5} \). This will effectively eliminate the fraction on the left side of the equation.
In terms of division, if you wanted to think of it that way (though it's not necessary here), you would be dividing both sides by \( \frac{5}{8} \). Dividing by a fraction is equivalent to multiplying by its reciprocal.
Thus, the answer is that both sides should be multiplied by \( \frac{8}{5} \) (or you could say divided by \( \frac{5}{8} \) if you prefer that perspective).