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Simplifying 12(z + 1) + -3(z + -4) = 4(z + -4) + 4(z + -4) Reorder the terms: 12(1 + z) + -3(z + -4) = 4(z + -4) + 4(z + -4) (1 * 12 + z * 12) + -3(z + -4) = 4(z + -4) + 4(z + -4) (12 + 12z) + -3(z + -4) = 4(z + -4) + 4(z + -4) Reorder the terms: 12 + 12z + -3(-4 + z) = 4(z + -4) + 4(z + -4) 12 + 12z + (-4 * -3 + z * -3) = 4(z + -4) + 4(z + -4) 12 + 12z + (12 + -3z) = 4(z + -4) + 4(z + -4) Reorder the terms: 12 + 12 + 12z + -3z = 4(z + -4) + 4(z + -4) Combine like terms: 12 + 12 = 24 24 + 12z + -3z = 4(z + -4) + 4(z + -4) Combine like terms: 12z + -3z = 9z 24 + 9z = 4(z + -4) + 4(z + -4) Reorder the terms: 24 + 9z = 4(-4 + z) + 4(z + -4) 24 + 9z = (-4 * 4 + z * 4) + 4(z + -4) 24 + 9z = (-16 + 4z) + 4(z + -4) Reorder the terms: 24 + 9z = -16 + 4z + 4(-4 + z) 24 + 9z = -16 + 4z + (-4 * 4 + z * 4) 24 + 9z = -16 + 4z + (-16 + 4z) Reorder the terms: 24 + 9z = -16 + -16 + 4z + 4z Combine like terms: -16 + -16 = -32 24 + 9z = -32 + 4z + 4z Combine like terms: 4z + 4z = 8z 24 + 9z = -32 + 8z Solving 24 + 9z = -32 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. 24 + 9z + -8z = -32 + 8z + -8z Combine like terms: 9z + -8z = 1z 24 + 1z = -32 + 8z + -8z Combine like terms: 8z + -8z = 0 24 + 1z = -32 + 0 24 + 1z = -32 Add '-24' to each side of the equation. 24 + -24 + 1z = -32 + -24 Combine like terms: 24 + -24 = 0 0 + 1z = -32 + -24 1z = -32 + -24 Combine like terms: -32 + -24 = -56 1z = -56 Divide each side by '1'. z = -56 Simplifying z = -56
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