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3z-7=7z-47
We move all terms to the left:
3z-7-(7z-47)=0
We get rid of parentheses
3z-7z+47-7=0
We add all the numbers together, and all the variables
-4z+40=0
We move all terms containing z to the left, all other terms to the right
-4z=-40
z=-40/-4
z=+10
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