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Simplifying 3(5Z + -1) + -5(Z + 2) = 7(Z + 1) Reorder the terms: 3(-1 + 5Z) + -5(Z + 2) = 7(Z + 1) (-1 * 3 + 5Z * 3) + -5(Z + 2) = 7(Z + 1) (-3 + 15Z) + -5(Z + 2) = 7(Z + 1) Reorder the terms: -3 + 15Z + -5(2 + Z) = 7(Z + 1) -3 + 15Z + (2 * -5 + Z * -5) = 7(Z + 1) -3 + 15Z + (-10 + -5Z) = 7(Z + 1) Reorder the terms: -3 + -10 + 15Z + -5Z = 7(Z + 1) Combine like terms: -3 + -10 = -13 -13 + 15Z + -5Z = 7(Z + 1) Combine like terms: 15Z + -5Z = 10Z -13 + 10Z = 7(Z + 1) Reorder the terms: -13 + 10Z = 7(1 + Z) -13 + 10Z = (1 * 7 + Z * 7) -13 + 10Z = (7 + 7Z) Solving -13 + 10Z = 7 + 7Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-7Z' to each side of the equation. -13 + 10Z + -7Z = 7 + 7Z + -7Z Combine like terms: 10Z + -7Z = 3Z -13 + 3Z = 7 + 7Z + -7Z Combine like terms: 7Z + -7Z = 0 -13 + 3Z = 7 + 0 -13 + 3Z = 7 Add '13' to each side of the equation. -13 + 13 + 3Z = 7 + 13 Combine like terms: -13 + 13 = 0 0 + 3Z = 7 + 13 3Z = 7 + 13 Combine like terms: 7 + 13 = 20 3Z = 20 Divide each side by '3'. Z = 6.666666667 Simplifying Z = 6.666666667
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