User:Forrest-HTX/Iceman's Paradox

During math class, Iceman said that by multiplying by 0 on both sides, everything will always be equal.

Proof: 1 + 3x = 2x + 3

in other words

x = 2

Now I multiply by 2 on both sides

(1 + 3x)×2 = (2x + 3)×2

2+6x = 4x+6

which means

2x = 4

and reduced

x = 2

Now I multiply by 0

(1 + 3x)×0 = (2x + 3)×0

Which means

0=0

This is also correct

but..

If we take this clearly wrong equation

1 + 3x = 3x + 3

we get that

1 = 3

which is wrong

but..

if we multiply by 0 on both sides

(1 + 3x)×0 = (3x + 3)×0

we get that

0=0

which was correct before