x = 0.999... This equation is giving me a headache; what am I doing wrong?

I encountered this equation in r/fifthworldproblems and its been bothering me ever since. So what happens when I try to turn it into a fraction is:

x = 0.9999...

10x = 9.9999...

10x - x = 9.999... - 0.9999...

9x = 9

x = 9/9?

x = 1?

What am I doing wrong?