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Solve for z
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0.5z+4.1-4.6z=0
Subtract 4.6z from both sides.
-4.1z+4.1=0
Combine 0.5z and -4.6z to get -4.1z.
-4.1z=-4.1
Subtract 4.1 from both sides. Anything subtracted from zero gives its negation.
z=\frac{-4.1}{-4.1}
Divide both sides by -4.1.
z=1
Divide -4.1 by -4.1 to get 1.