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-3z+7=5z-1
We move all terms to the left:
-3z+7-(5z-1)=0
We get rid of parentheses
-3z-5z+1+7=0
We add all the numbers together, and all the variables
-8z+8=0
We move all terms containing z to the left, all other terms to the right
-8z=-8
z=-8/-8
z=1
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