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