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5x+7=10x+47
We move all terms to the left:
5x+7-(10x+47)=0
We get rid of parentheses
5x-10x-47+7=0
We add all the numbers together, and all the variables
-5x-40=0
We move all terms containing x to the left, all other terms to the right
-5x=40
x=40/-5
x=-8
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