Prove or Disprove: for All Real Numbers $x$ And $y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x\rfloor$

Prove or disprove: For all real numbers $x$ and $y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x\rfloor$