If\[f(x) = \begin{cases} 2x-5 &\quad \text{if } x \ge 3, \\ -x + 5 &\quad \text{if } x < 3, \end{cases} \]then for how many values of $x$ is $f(f(x)) = 3$?

The only solultion is x = 1, so there is only one solution.

its seems that answer is incorrect but thanks for trying

The following graphs should help: