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Simplifying 5(3Z + -1) + -3(Z + 9) = 5(Z + 1) Reorder the terms: 5(-1 + 3Z) + -3(Z + 9) = 5(Z + 1) (-1 * 5 + 3Z * 5) + -3(Z + 9) = 5(Z + 1) (-5 + 15Z) + -3(Z + 9) = 5(Z + 1) Reorder the terms: -5 + 15Z + -3(9 + Z) = 5(Z + 1) -5 + 15Z + (9 * -3 + Z * -3) = 5(Z + 1) -5 + 15Z + (-27 + -3Z) = 5(Z + 1) Reorder the terms: -5 + -27 + 15Z + -3Z = 5(Z + 1) Combine like terms: -5 + -27 = -32 -32 + 15Z + -3Z = 5(Z + 1) Combine like terms: 15Z + -3Z = 12Z -32 + 12Z = 5(Z + 1) Reorder the terms: -32 + 12Z = 5(1 + Z) -32 + 12Z = (1 * 5 + Z * 5) -32 + 12Z = (5 + 5Z) Solving -32 + 12Z = 5 + 5Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-5Z' to each side of the equation. -32 + 12Z + -5Z = 5 + 5Z + -5Z Combine like terms: 12Z + -5Z = 7Z -32 + 7Z = 5 + 5Z + -5Z Combine like terms: 5Z + -5Z = 0 -32 + 7Z = 5 + 0 -32 + 7Z = 5 Add '32' to each side of the equation. -32 + 32 + 7Z = 5 + 32 Combine like terms: -32 + 32 = 0 0 + 7Z = 5 + 32 7Z = 5 + 32 Combine like terms: 5 + 32 = 37 7Z = 37 Divide each side by '7'. Z = 5.285714286 Simplifying Z = 5.285714286
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