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-4(z-3)=7z+1
We move all terms to the left:
-4(z-3)-(7z+1)=0
We multiply parentheses
-4z-(7z+1)+12=0
We get rid of parentheses
-4z-7z-1+12=0
We add all the numbers together, and all the variables
-11z+11=0
We move all terms containing z to the left, all other terms to the right
-11z=-11
z=-11/-11
z=1
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