There are several developers working towards this right now! Unfortunately most of these projects are still in the "Crowdfunding" or "Pre-order" stages.
One promising board, the "UP-Board" currently on Pre-Order: http://www.up-board.org/
- $99
- 2GB RAM
- 16GB EMMC memory
- Intel processor (Compatible with Windows 8.1/10, Unknown if compatible with Linux)
Another promising board, the "Lattepanda" currently still in the Pre-Order stage located here
- $89
- 2GB RAM
- 32GB EMMC memory
- Intel atom (quad-core) processor (Compatible with Windows 8.1/10, Linux various)
Honorable mentions:
If you are looking for a board that is currently available at your price point and also X86, you are out of luck. However, if you upped your price point by between $50-$100, you'd find some neat boards on Amazon
NOTE: I am involved with the Lattepanda project as a backer, however I do not own or operate it.