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Simplifying 5(4Z + -1) + -3(2 + 7) = 14(Z + 1) Reorder the terms: 5(-1 + 4Z) + -3(2 + 7) = 14(Z + 1) (-1 * 5 + 4Z * 5) + -3(2 + 7) = 14(Z + 1) (-5 + 20Z) + -3(2 + 7) = 14(Z + 1) Combine like terms: 2 + 7 = 9 -5 + 20Z + -3(9) = 14(Z + 1) Multiply -3 * 9 -5 + 20Z + -27 = 14(Z + 1) Reorder the terms: -5 + -27 + 20Z = 14(Z + 1) Combine like terms: -5 + -27 = -32 -32 + 20Z = 14(Z + 1) Reorder the terms: -32 + 20Z = 14(1 + Z) -32 + 20Z = (1 * 14 + Z * 14) -32 + 20Z = (14 + 14Z) Solving -32 + 20Z = 14 + 14Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-14Z' to each side of the equation. -32 + 20Z + -14Z = 14 + 14Z + -14Z Combine like terms: 20Z + -14Z = 6Z -32 + 6Z = 14 + 14Z + -14Z Combine like terms: 14Z + -14Z = 0 -32 + 6Z = 14 + 0 -32 + 6Z = 14 Add '32' to each side of the equation. -32 + 32 + 6Z = 14 + 32 Combine like terms: -32 + 32 = 0 0 + 6Z = 14 + 32 6Z = 14 + 32 Combine like terms: 14 + 32 = 46 6Z = 46 Divide each side by '6'. Z = 7.666666667 Simplifying Z = 7.666666667
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