|f(x) + g(x)| = |f(x)| + |g(x)|
Putting value of f(x) and g(x), we get,
|2x-5| + |7-2x| = 2
1st Case: When x<=5/2
-2x + 5 +7 – 2x = 2
=> x=5/2
2nd Case: 5/2 < x < 7/2
On solving, we get, 2=2, which satisfies the condition
3rd Case: x ≥ 7/2
2x-5 – 7+2x = 2
x=7/2
So, the answer should be 5/2<= x <= 7/2
Option (D)