To find the value of \( x \) when \( f(x) = 3 \), we set the equation as follows:
\[ f(x) = x - 7 \]
Setting \( f(x) \) equal to 3, we have:
\[ x - 7 = 3 \]
Now, add 7 to both sides:
\[ x = 3 + 7 \]
\[ x = 10 \]
Therefore, the value of \( x \) when \( f(x) = 3 \) is \( \boxed{10} \).