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x+10=-6x+3
We move all terms to the left:
x+10-(-6x+3)=0
We get rid of parentheses
x+6x-3+10=0
We add all the numbers together, and all the variables
7x+7=0
We move all terms containing x to the left, all other terms to the right
7x=-7
x=-7/7
x=-1
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