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Simplifying 3(6z + -1) + -2(z + 2) = 13(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 2) = 13(z + 1) (-1 * 3 + 6z * 3) + -2(z + 2) = 13(z + 1) (-3 + 18z) + -2(z + 2) = 13(z + 1) Reorder the terms: -3 + 18z + -2(2 + z) = 13(z + 1) -3 + 18z + (2 * -2 + z * -2) = 13(z + 1) -3 + 18z + (-4 + -2z) = 13(z + 1) Reorder the terms: -3 + -4 + 18z + -2z = 13(z + 1) Combine like terms: -3 + -4 = -7 -7 + 18z + -2z = 13(z + 1) Combine like terms: 18z + -2z = 16z -7 + 16z = 13(z + 1) Reorder the terms: -7 + 16z = 13(1 + z) -7 + 16z = (1 * 13 + z * 13) -7 + 16z = (13 + 13z) Solving -7 + 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. -7 + 16z + -13z = 13 + 13z + -13z Combine like terms: 16z + -13z = 3z -7 + 3z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -7 + 3z = 13 + 0 -7 + 3z = 13 Add '7' to each side of the equation. -7 + 7 + 3z = 13 + 7 Combine like terms: -7 + 7 = 0 0 + 3z = 13 + 7 3z = 13 + 7 Combine like terms: 13 + 7 = 20 3z = 20 Divide each side by '3'. z = 6.666666667 Simplifying z = 6.666666667
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