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Simplifying 3(4Z + -1) + -4(Z + 8) = 3(Z + 1) Reorder the terms: 3(-1 + 4Z) + -4(Z + 8) = 3(Z + 1) (-1 * 3 + 4Z * 3) + -4(Z + 8) = 3(Z + 1) (-3 + 12Z) + -4(Z + 8) = 3(Z + 1) Reorder the terms: -3 + 12Z + -4(8 + Z) = 3(Z + 1) -3 + 12Z + (8 * -4 + Z * -4) = 3(Z + 1) -3 + 12Z + (-32 + -4Z) = 3(Z + 1) Reorder the terms: -3 + -32 + 12Z + -4Z = 3(Z + 1) Combine like terms: -3 + -32 = -35 -35 + 12Z + -4Z = 3(Z + 1) Combine like terms: 12Z + -4Z = 8Z -35 + 8Z = 3(Z + 1) Reorder the terms: -35 + 8Z = 3(1 + Z) -35 + 8Z = (1 * 3 + Z * 3) -35 + 8Z = (3 + 3Z) Solving -35 + 8Z = 3 + 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. -35 + 8Z + -3Z = 3 + 3Z + -3Z Combine like terms: 8Z + -3Z = 5Z -35 + 5Z = 3 + 3Z + -3Z Combine like terms: 3Z + -3Z = 0 -35 + 5Z = 3 + 0 -35 + 5Z = 3 Add '35' to each side of the equation. -35 + 35 + 5Z = 3 + 35 Combine like terms: -35 + 35 = 0 0 + 5Z = 3 + 35 5Z = 3 + 35 Combine like terms: 3 + 35 = 38 5Z = 38 Divide each side by '5'. Z = 7.6 Simplifying Z = 7.6

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