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Simplifying 5(4z + -1) + -5(z + 1) = 8(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 1) = 8(z + 1) (-1 * 5 + 4z * 5) + -5(z + 1) = 8(z + 1) (-5 + 20z) + -5(z + 1) = 8(z + 1) Reorder the terms: -5 + 20z + -5(1 + z) = 8(z + 1) -5 + 20z + (1 * -5 + z * -5) = 8(z + 1) -5 + 20z + (-5 + -5z) = 8(z + 1) Reorder the terms: -5 + -5 + 20z + -5z = 8(z + 1) Combine like terms: -5 + -5 = -10 -10 + 20z + -5z = 8(z + 1) Combine like terms: 20z + -5z = 15z -10 + 15z = 8(z + 1) Reorder the terms: -10 + 15z = 8(1 + z) -10 + 15z = (1 * 8 + z * 8) -10 + 15z = (8 + 8z) Solving -10 + 15z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -10 + 15z + -8z = 8 + 8z + -8z Combine like terms: 15z + -8z = 7z -10 + 7z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -10 + 7z = 8 + 0 -10 + 7z = 8 Add '10' to each side of the equation. -10 + 10 + 7z = 8 + 10 Combine like terms: -10 + 10 = 0 0 + 7z = 8 + 10 7z = 8 + 10 Combine like terms: 8 + 10 = 18 7z = 18 Divide each side by '7'. z = 2.571428571 Simplifying z = 2.571428571
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