okay andrew

Umm...9x does equal 8.99999...1. Sure 10x=9.99999 but that has nothing to do with 9x. Plus, 0.3333 doesn't equal 1/3; it's close, but it's ever so slightly off, as is 0.99999... so substituting 0.333333... with 1/3 is also an entirely different, although similar. equation. Just because 1/3*3=1 doesn't mean that 0.3333...*3=1.

To show you that it works, or else you'd say that 9x = 89999...1 or something. But if you won't take this, then there's another way.

1/3 = 0.3333...

0.3333...*3 = 0.9999....

(1/3)*3 = 1

By the transitive property, then, 0.9999... = 1.

9.9999999....-0.999999... doesn't equal 9 x 0.999999999
Plus there was no point in saying x=0.9999999 in your equation because you never incorporated it in 9x=9; you just solved for x. What was the point of saying 10x= 9.999999?

And if it doesn't equal 9, what DOES it equal?