Wall is not flat

We are in the middle of a bathroom renovation. We wanted to purchase a pre made granite countertop and backsplash. We have removed a tile counter and will be removing the backsplash. We have determined that the wall is not flat. We think the 2 X 4 about 18" away from the wall is bowed and so the wall bows out. It angles out up to 1/2"+ by the time it get to the wall. I've tried to search this situation and can't find a solution. I'm sure this must happen. If we put up the flat back splash there's going to be a huge gap....too big to look decent if we fill it with silicone. Here is a link to a picture. You can see the large gap. We placed a straight board against the wall. https://picasaweb.google.com/hillbie...eat=directlink

 

Wow. That's a bad one. Is this an interior or exterior wall? Is this a hump in the wall, or is the wall basically straight until you get into the corner?

It's common for granite installers to remove the drywall in areas where there is a hump to get their stone in. I'm not sure this technique will look good for your application. Even if you split the difference and put the back splash a 1/4" into the wall and fill the 1/4" gap it will be very noticeable.

Consider filling that dip in with joint compound and feathering it out so it looks good.

 

If you do decide to try and build up/fill and feather that 1/2 inch gap I would use a high strength product such as Durabond to avoid compound cracking issues later. You can finish coat with normal drywall compound in this case but be careful with your first coat of Durabond to trowel it and feather it out as smooth as possible. It takes alot of work to sand it smooth once it hardens compared to the regular products.