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Simplifying 6(4Z + -1) + -5(Z + 5) = 12(Z + 1) Reorder the terms: 6(-1 + 4Z) + -5(Z + 5) = 12(Z + 1) (-1 * 6 + 4Z * 6) + -5(Z + 5) = 12(Z + 1) (-6 + 24Z) + -5(Z + 5) = 12(Z + 1) Reorder the terms: -6 + 24Z + -5(5 + Z) = 12(Z + 1) -6 + 24Z + (5 * -5 + Z * -5) = 12(Z + 1) -6 + 24Z + (-25 + -5Z) = 12(Z + 1) Reorder the terms: -6 + -25 + 24Z + -5Z = 12(Z + 1) Combine like terms: -6 + -25 = -31 -31 + 24Z + -5Z = 12(Z + 1) Combine like terms: 24Z + -5Z = 19Z -31 + 19Z = 12(Z + 1) Reorder the terms: -31 + 19Z = 12(1 + Z) -31 + 19Z = (1 * 12 + Z * 12) -31 + 19Z = (12 + 12Z) Solving -31 + 19Z = 12 + 12Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-12Z' to each side of the equation. -31 + 19Z + -12Z = 12 + 12Z + -12Z Combine like terms: 19Z + -12Z = 7Z -31 + 7Z = 12 + 12Z + -12Z Combine like terms: 12Z + -12Z = 0 -31 + 7Z = 12 + 0 -31 + 7Z = 12 Add '31' to each side of the equation. -31 + 31 + 7Z = 12 + 31 Combine like terms: -31 + 31 = 0 0 + 7Z = 12 + 31 7Z = 12 + 31 Combine like terms: 12 + 31 = 43 7Z = 43 Divide each side by '7'. Z = 6.142857143 Simplifying Z = 6.142857143
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