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Simplifying 4(3z + 7) + 3(5z + 1) = 54 Reorder the terms: 4(7 + 3z) + 3(5z + 1) = 54 (7 * 4 + 3z * 4) + 3(5z + 1) = 54 (28 + 12z) + 3(5z + 1) = 54 Reorder the terms: 28 + 12z + 3(1 + 5z) = 54 28 + 12z + (1 * 3 + 5z * 3) = 54 28 + 12z + (3 + 15z) = 54 Reorder the terms: 28 + 3 + 12z + 15z = 54 Combine like terms: 28 + 3 = 31 31 + 12z + 15z = 54 Combine like terms: 12z + 15z = 27z 31 + 27z = 54 Solving 31 + 27z = 54 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 27z = 54 + -31 Combine like terms: 31 + -31 = 0 0 + 27z = 54 + -31 27z = 54 + -31 Combine like terms: 54 + -31 = 23 27z = 23 Divide each side by '27'. z = 0.8518518519 Simplifying z = 0.8518518519
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