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Simplifying 3(6z + -1) + -2(z + 9) = 13(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 9) = 13(z + 1) (-1 * 3 + 6z * 3) + -2(z + 9) = 13(z + 1) (-3 + 18z) + -2(z + 9) = 13(z + 1) Reorder the terms: -3 + 18z + -2(9 + z) = 13(z + 1) -3 + 18z + (9 * -2 + z * -2) = 13(z + 1) -3 + 18z + (-18 + -2z) = 13(z + 1) Reorder the terms: -3 + -18 + 18z + -2z = 13(z + 1) Combine like terms: -3 + -18 = -21 -21 + 18z + -2z = 13(z + 1) Combine like terms: 18z + -2z = 16z -21 + 16z = 13(z + 1) Reorder the terms: -21 + 16z = 13(1 + z) -21 + 16z = (1 * 13 + z * 13) -21 + 16z = (13 + 13z) Solving -21 + 16z = 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. -21 + 16z + -13z = 13 + 13z + -13z Combine like terms: 16z + -13z = 3z -21 + 3z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -21 + 3z = 13 + 0 -21 + 3z = 13 Add '21' to each side of the equation. -21 + 21 + 3z = 13 + 21 Combine like terms: -21 + 21 = 0 0 + 3z = 13 + 21 3z = 13 + 21 Combine like terms: 13 + 21 = 34 3z = 34 Divide each side by '3'. z = 11.33333333 Simplifying z = 11.33333333
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