Lunar Phase Range

Although the Moon is moving eastward around the Earth, the Earth is also turning to the east and much faster, for it goes all the way around its axis of rotation in just under a day.

As a result, although the Moon is moving to the east relative to the stars, the much faster westward motion of the sky is carrying it to the west, so despite its eastward motion relative to the center of the Earth, it rises in the east and sets in the west, just like any other celestial body.

http://cseligman.com/text/sky/moonmotion.htm