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How to install tile backsplash on uneven wall.
Mark the wall at the top of the tile.
Slightly rock the sheet up and down perpendicular to the trowel lines to collapse the ridges and help the tile settle into place.
Spread thinset mortar on the bottom center of the wall.
Shop for tile tools.
This ensures the tile adhesive secures to the surface.
Place the mosaic sheets along the wall.
Secure the drop cloth on the counter using the painter s tape covering the entire work area.
If your cabinets are farther than 24 away from wall then you won t have excess on backsplash to trim off.
Backsplash installation in 15 steps.
Then use a level to extend the line along the work area.
Spread the mortar with the flat edge of the trowel then groove.
Apply grout with a rubber float working diagonally across the tile.
Back buttering back buttering is a trick used for tiles of uneven thickness like ungauged slate or handmade tiles extremely large tiles or for tiles being installed on an uneven surface.
Hold a tile at this spot accounting for a 1 8 inch expansion gap.
While you volunteered to set tiles is repairing rebuilding the wall something you even want to deal with.
Hold the float at a 45 degree angle as you work the grout into the seams.
Shop for grout and mortar.
A professional installer would use a pair of scribes to transfer the contour of the wall onto the top edge of the counter top then use a circular saw or a belt sander to take off the area of the backsplash where your wall is bowed out.
Shop for tile.
Mark the two sides of the wall using the painter s tape where the backsplash should.
Follow the lines you made when the tiles were dry fit to the wall.
Clean the wall thoroughly with the cleaner to remove any grease or other debris.
Do not grout the bottom seam where the tile meets the countertop you ll want to use caulk in that seam.
Wash the wall with tsp tri sodium phosphate or an ammonia based cleaner to remove any grease or oil.
Use the float to take off any excess grout then allow the grout to set for 10 minutes.
Use tile spacers if necessary to keep the tile lines straight in the layout.
If existing tiles are beyond repair remove the tile and install a piece of wallboard in its place.
That is what i would do so it could be painted i would not even try to tile over the patch job you described.
First use a level to find the lowest point of the countertop.
Like bill pointed out you are unlikely to end up with a flat enough surface to get a good tile job unless you use very small tiles.