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Simplifying 4(z + 1) + 5(4 + -1z) = 3z + -8 Reorder the terms: 4(1 + z) + 5(4 + -1z) = 3z + -8 (1 * 4 + z * 4) + 5(4 + -1z) = 3z + -8 (4 + 4z) + 5(4 + -1z) = 3z + -8 4 + 4z + (4 * 5 + -1z * 5) = 3z + -8 4 + 4z + (20 + -5z) = 3z + -8 Reorder the terms: 4 + 20 + 4z + -5z = 3z + -8 Combine like terms: 4 + 20 = 24 24 + 4z + -5z = 3z + -8 Combine like terms: 4z + -5z = -1z 24 + -1z = 3z + -8 Reorder the terms: 24 + -1z = -8 + 3z Solving 24 + -1z = -8 + 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. 24 + -1z + -3z = -8 + 3z + -3z Combine like terms: -1z + -3z = -4z 24 + -4z = -8 + 3z + -3z Combine like terms: 3z + -3z = 0 24 + -4z = -8 + 0 24 + -4z = -8 Add '-24' to each side of the equation. 24 + -24 + -4z = -8 + -24 Combine like terms: 24 + -24 = 0 0 + -4z = -8 + -24 -4z = -8 + -24 Combine like terms: -8 + -24 = -32 -4z = -32 Divide each side by '-4'. z = 8 Simplifying z = 8
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