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Simplifying 4(5z + -1) + -5(z + 6) = 13(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 6) = 13(z + 1) (-1 * 4 + 5z * 4) + -5(z + 6) = 13(z + 1) (-4 + 20z) + -5(z + 6) = 13(z + 1) Reorder the terms: -4 + 20z + -5(6 + z) = 13(z + 1) -4 + 20z + (6 * -5 + z * -5) = 13(z + 1) -4 + 20z + (-30 + -5z) = 13(z + 1) Reorder the terms: -4 + -30 + 20z + -5z = 13(z + 1) Combine like terms: -4 + -30 = -34 -34 + 20z + -5z = 13(z + 1) Combine like terms: 20z + -5z = 15z -34 + 15z = 13(z + 1) Reorder the terms: -34 + 15z = 13(1 + z) -34 + 15z = (1 * 13 + z * 13) -34 + 15z = (13 + 13z) Solving -34 + 15z = 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. -34 + 15z + -13z = 13 + 13z + -13z Combine like terms: 15z + -13z = 2z -34 + 2z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -34 + 2z = 13 + 0 -34 + 2z = 13 Add '34' to each side of the equation. -34 + 34 + 2z = 13 + 34 Combine like terms: -34 + 34 = 0 0 + 2z = 13 + 34 2z = 13 + 34 Combine like terms: 13 + 34 = 47 2z = 47 Divide each side by '2'. z = 23.5 Simplifying z = 23.5
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