To determine how many solutions the equation \( \frac{4x - 10}{2} = 2x - 5 \) has, we can first simplify the equation.
Starting with the left side:
\[ \frac{4x - 10}{2} = \frac{4x}{2} - \frac{10}{2} = 2x - 5 \]
Now, the equation simplifies to:
\[ 2x - 5 = 2x - 5 \]
Since both sides of the equation are identical, this means that the equation is true for any value of \( x \).
This indicates that there are infinitely many solutions.
The correct answer is:
D. infinitely many solutions