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Simplifying 4(5z + -1) + -4(z + 9) = 13(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 9) = 13(z + 1) (-1 * 4 + 5z * 4) + -4(z + 9) = 13(z + 1) (-4 + 20z) + -4(z + 9) = 13(z + 1) Reorder the terms: -4 + 20z + -4(9 + z) = 13(z + 1) -4 + 20z + (9 * -4 + z * -4) = 13(z + 1) -4 + 20z + (-36 + -4z) = 13(z + 1) Reorder the terms: -4 + -36 + 20z + -4z = 13(z + 1) Combine like terms: -4 + -36 = -40 -40 + 20z + -4z = 13(z + 1) Combine like terms: 20z + -4z = 16z -40 + 16z = 13(z + 1) Reorder the terms: -40 + 16z = 13(1 + z) -40 + 16z = (1 * 13 + z * 13) -40 + 16z = (13 + 13z) Solving -40 + 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. -40 + 16z + -13z = 13 + 13z + -13z Combine like terms: 16z + -13z = 3z -40 + 3z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -40 + 3z = 13 + 0 -40 + 3z = 13 Add '40' to each side of the equation. -40 + 40 + 3z = 13 + 40 Combine like terms: -40 + 40 = 0 0 + 3z = 13 + 40 3z = 13 + 40 Combine like terms: 13 + 40 = 53 3z = 53 Divide each side by '3'. z = 17.66666667 Simplifying z = 17.66666667
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