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Simplifying 4(5z + -1) + -3(z + 6) = 13(z + 1) Reorder the terms: 4(-1 + 5z) + -3(z + 6) = 13(z + 1) (-1 * 4 + 5z * 4) + -3(z + 6) = 13(z + 1) (-4 + 20z) + -3(z + 6) = 13(z + 1) Reorder the terms: -4 + 20z + -3(6 + z) = 13(z + 1) -4 + 20z + (6 * -3 + z * -3) = 13(z + 1) -4 + 20z + (-18 + -3z) = 13(z + 1) Reorder the terms: -4 + -18 + 20z + -3z = 13(z + 1) Combine like terms: -4 + -18 = -22 -22 + 20z + -3z = 13(z + 1) Combine like terms: 20z + -3z = 17z -22 + 17z = 13(z + 1) Reorder the terms: -22 + 17z = 13(1 + z) -22 + 17z = (1 * 13 + z * 13) -22 + 17z = (13 + 13z) Solving -22 + 17z = 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. -22 + 17z + -13z = 13 + 13z + -13z Combine like terms: 17z + -13z = 4z -22 + 4z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -22 + 4z = 13 + 0 -22 + 4z = 13 Add '22' to each side of the equation. -22 + 22 + 4z = 13 + 22 Combine like terms: -22 + 22 = 0 0 + 4z = 13 + 22 4z = 13 + 22 Combine like terms: 13 + 22 = 35 4z = 35 Divide each side by '4'. z = 8.75 Simplifying z = 8.75
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