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12x-1=6x+1=
We move all terms to the left:
12x-1-(6x+1)=0
We get rid of parentheses
12x-6x-1-1=0
We add all the numbers together, and all the variables
6x-2=0
We move all terms containing x to the left, all other terms to the right
6x=2
x=2/6
x=1/3
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