Mathematica 9.0.1 on Windows 7 64 bit does it
In[5]:= Reduce[(2 x + 1)^2 - (x - 3)^2 >= 2 (x - 1) (x + 2) - 11, x]
Out[5]= x <= -7 || x >= -1
ordering an inequality forces x to be an integer, rational number or a real one. What happens if you state the tautology in your version
In[8]:= Reduce[(2 x + 1)^2 - (x - 3)^2 >= 2 (x - 1) (x + 2) - 11, x, Reals]
Out[8]= x <= -7 || x >= -1
