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Simplifying 4(5z + -1) + -4(z + 3) = 13(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 3) = 13(z + 1) (-1 * 4 + 5z * 4) + -4(z + 3) = 13(z + 1) (-4 + 20z) + -4(z + 3) = 13(z + 1) Reorder the terms: -4 + 20z + -4(3 + z) = 13(z + 1) -4 + 20z + (3 * -4 + z * -4) = 13(z + 1) -4 + 20z + (-12 + -4z) = 13(z + 1) Reorder the terms: -4 + -12 + 20z + -4z = 13(z + 1) Combine like terms: -4 + -12 = -16 -16 + 20z + -4z = 13(z + 1) Combine like terms: 20z + -4z = 16z -16 + 16z = 13(z + 1) Reorder the terms: -16 + 16z = 13(1 + z) -16 + 16z = (1 * 13 + z * 13) -16 + 16z = (13 + 13z) Solving -16 + 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. -16 + 16z + -13z = 13 + 13z + -13z Combine like terms: 16z + -13z = 3z -16 + 3z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -16 + 3z = 13 + 0 -16 + 3z = 13 Add '16' to each side of the equation. -16 + 16 + 3z = 13 + 16 Combine like terms: -16 + 16 = 0 0 + 3z = 13 + 16 3z = 13 + 16 Combine like terms: 13 + 16 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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