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Simplifying 0.5(8z + 12) + -5 = 3(z + -8) Reorder the terms: 0.5(12 + 8z) + -5 = 3(z + -8) (12 * 0.5 + 8z * 0.5) + -5 = 3(z + -8) (6 + 4z) + -5 = 3(z + -8) Reorder the terms: 6 + -5 + 4z = 3(z + -8) Combine like terms: 6 + -5 = 1 1 + 4z = 3(z + -8) Reorder the terms: 1 + 4z = 3(-8 + z) 1 + 4z = (-8 * 3 + z * 3) 1 + 4z = (-24 + 3z) Solving 1 + 4z = -24 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 1 + 4z + -3z = -24 + 3z + -3z Combine like terms: 4z + -3z = 1z 1 + 1z = -24 + 3z + -3z Combine like terms: 3z + -3z = 0 1 + 1z = -24 + 0 1 + 1z = -24 Add '-1' to each side of the equation. 1 + -1 + 1z = -24 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = -24 + -1 1z = -24 + -1 Combine like terms: -24 + -1 = -25 1z = -25 Divide each side by '1'. z = -25 Simplifying z = -25
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