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6(x-2)=x-3
We move all terms to the left:
6(x-2)-(x-3)=0
We multiply parentheses
6x-(x-3)-12=0
We get rid of parentheses
6x-x+3-12=0
We add all the numbers together, and all the variables
5x-9=0
We move all terms containing x to the left, all other terms to the right
5x=9
x=9/5
x=1+4/5
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