one equals point nine repeating forever

.9... = point 9 repeating forever

x = .9...

multiply both sides by 10
10x = 9.9...

subtract x from both sides (remember x = .9...)
10x - x = 9.9... - x

to get
9x = 9

now divide both sides by 9
9x/9 = 9/9

and the result is
x = 1

therefore
1 = .9...