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4(x)=7x+1
We move all terms to the left:
4(x)-(7x+1)=0
We get rid of parentheses
4x-7x-1=0
We add all the numbers together, and all the variables
-3x-1=0
We move all terms containing x to the left, all other terms to the right
-3x=1
x=1/-3
x=-1/3
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