My guess is that since x appears in both sides of
x >= -Subscript[OverBar[x], C] + Subscript[OverBar[x], T]
that the condition never resolves to True. So, for example,
With[
{x = 0},
x >= -Subscript[OverBar[x], C] + Subscript[OverBar[x], T]]
gives
0 >= -Subscript[OverBar[0], C] + Subscript[OverBar[0], T]
which is not True.
