0.999....=1

[Peh]

Davman said:
The problem is that you don't understand you cannot replace 0,999.... with x during the solution.

And the winner is this guy.

It's midnight here and I can' think straight. The calculation is wrong in the op. You can't add an x out of nothing on one side and remove 0.9999999. That's the mistake OP did. 

 

So you had to +x on both sides and minus 0.9999 also on both sides. You just can't replace 0,99999 with X. This is not possible.