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x+1=7x+7
We move all terms to the left:
x+1-(7x+7)=0
We get rid of parentheses
x-7x-7+1=0
We add all the numbers together, and all the variables
-6x-6=0
We move all terms containing x to the left, all other terms to the right
-6x=6
x=6/-6
x=-1
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