a = x
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]
2 = 1. Problem?
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]
2 = 1. Problem?
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Sigh, you and a billion other people have posted problems nearly identical to this thinking they were clever. If you were clever you could figure out the very obvious flaw in the work.
Pointing out that a-x = 0
2(a-x) = (a-x)
2*0 = 1*0
Next, you divide both sides by a-x = 0
2*0/0 = 1*0/0
ERROR: Divide by 0, doesn't work.
Edit:
a=x can be reworked as
0= a-x
The problem with the forumula becomes clear as soon as you replace a-x with 0.
Pointing out that a-x = 0
2(a-x) = (a-x)
2*0 = 1*0
Next, you divide both sides by a-x = 0
2*0/0 = 1*0/0
ERROR: Divide by 0, doesn't work.
Edit:
a=x can be reworked as
0= a-x
The problem with the forumula becomes clear as soon as you replace a-x with 0.