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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 = -25 -25 + 12z + 15z = 54 Combine like terms: 12z + 15z = 27z -25 + 27z = 54 Solving -25 + 27z = 54 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 27z = 54 + 25 Combine like terms: -25 + 25 = 0 0 + 27z = 54 + 25 27z = 54 + 25 Combine like terms: 54 + 25 = 79 27z = 79 Divide each side by '27'. z = 2.925925926 Simplifying z = 2.925925926
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