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Simplifying 5(9z + -3) + 7(2 + z) = 415 Reorder the terms: 5(-3 + 9z) + 7(2 + z) = 415 (-3 * 5 + 9z * 5) + 7(2 + z) = 415 (-15 + 45z) + 7(2 + z) = 415 -15 + 45z + (2 * 7 + z * 7) = 415 -15 + 45z + (14 + 7z) = 415 Reorder the terms: -15 + 14 + 45z + 7z = 415 Combine like terms: -15 + 14 = -1 -1 + 45z + 7z = 415 Combine like terms: 45z + 7z = 52z -1 + 52z = 415 Solving -1 + 52z = 415 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 52z = 415 + 1 Combine like terms: -1 + 1 = 0 0 + 52z = 415 + 1 52z = 415 + 1 Combine like terms: 415 + 1 = 416 52z = 416 Divide each side by '52'. z = 8 Simplifying z = 8
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