I have several applications where I rolled the carpet under itself about 2 inches with it butted tightly up against the tile. Then I tacked the carpet down with nails spaced about 1 inch apart.
Tucking it under raises the carpet up enough to make it somewhat level with the tile. This process eleminates the need for border strips, etc. Makes a good looking transition. If you have a difficult location, you may want a professional carpet layer to finish the job.
Good Luck!
Dodgeman