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Simplifying 3(6z + -1) + -3(z + 7) = 13(z + 1) Reorder the terms: 3(-1 + 6z) + -3(z + 7) = 13(z + 1) (-1 * 3 + 6z * 3) + -3(z + 7) = 13(z + 1) (-3 + 18z) + -3(z + 7) = 13(z + 1) Reorder the terms: -3 + 18z + -3(7 + z) = 13(z + 1) -3 + 18z + (7 * -3 + z * -3) = 13(z + 1) -3 + 18z + (-21 + -3z) = 13(z + 1) Reorder the terms: -3 + -21 + 18z + -3z = 13(z + 1) Combine like terms: -3 + -21 = -24 -24 + 18z + -3z = 13(z + 1) Combine like terms: 18z + -3z = 15z -24 + 15z = 13(z + 1) Reorder the terms: -24 + 15z = 13(1 + z) -24 + 15z = (1 * 13 + z * 13) -24 + 15z = (13 + 13z) Solving -24 + 15z = 13 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. -24 + 15z + -13z = 13 + 13z + -13z Combine like terms: 15z + -13z = 2z -24 + 2z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -24 + 2z = 13 + 0 -24 + 2z = 13 Add '24' to each side of the equation. -24 + 24 + 2z = 13 + 24 Combine like terms: -24 + 24 = 0 0 + 2z = 13 + 24 2z = 13 + 24 Combine like terms: 13 + 24 = 37 2z = 37 Divide each side by '2'. z = 18.5 Simplifying z = 18.5
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