How should I lay ceramic tile in a room where one side slants?
If you have a floor that is sinking or sagging, I would seriously consider whether it is sufficiently able to handle tile. If the floor has a bounce to it, you're going to constantly be having grout breaking out no matter whether you level it or not. Tile requires more infrastructure than other flooring options, so, without knowing I'd at least say reconsider or have an expert at least look at it for you first.