To solve the equation \( \frac{5}{8} (x - \frac{1}{2}) = 10 \), the first step involves reversing the multiplication by \( \frac{5}{8} \). This can be done by dividing both sides by \( \frac{5}{8} \).
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \( \frac{5}{8} \) is \( \frac{8}{5} \).
So, you will divide both sides of the equation by \( \frac{5}{8} \) to eliminate the fraction:
\[ x - \frac{1}{2} = 10 \times \frac{8}{5} \]
This will simplify the equation further, allowing you to isolate \( x \).