How do you handle the meeting of carpet to tile. My HT is carpeted and will be meeting floor tile at the door opening. Should the carpet be folded underneath itself and then attached with a tackless strip or should I just butt the carpet to the tile using a tackless strip and don't bother folding the carpet under?

I have a similar situation and the carpet guys used a rubber threshold piece that is about 1-1/2" wide, has an elevated side with a slot in it to accept the edge of the carpet and transitions to near flat on the other for the tile. It glues down to the subfloor. As I had this installed, can't direct you to anyone but I would think the local carpet store or maybe one of the two big box improvement stores might have them.

Found something that looks like it so you can get an idea of what you may be looking for.