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3z+2z-z=48
Multiply both sides of the equation by 6, the least common multiple of 2,3,6.
5z-z=48
Combine 3z and 2z to get 5z.
4z=48
Combine 5z and -z to get 4z.
z=\frac{48}{4}
Divide both sides by 4.
z=12
Divide 48 by 4 to get 12.