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Simplifying 4(5z + -1) + -5(z + 2) = 8(z + 1) Reorder the terms: 4(-1 + 5z) + -5(z + 2) = 8(z + 1) (-1 * 4 + 5z * 4) + -5(z + 2) = 8(z + 1) (-4 + 20z) + -5(z + 2) = 8(z + 1) Reorder the terms: -4 + 20z + -5(2 + z) = 8(z + 1) -4 + 20z + (2 * -5 + z * -5) = 8(z + 1) -4 + 20z + (-10 + -5z) = 8(z + 1) Reorder the terms: -4 + -10 + 20z + -5z = 8(z + 1) Combine like terms: -4 + -10 = -14 -14 + 20z + -5z = 8(z + 1) Combine like terms: 20z + -5z = 15z -14 + 15z = 8(z + 1) Reorder the terms: -14 + 15z = 8(1 + z) -14 + 15z = (1 * 8 + z * 8) -14 + 15z = (8 + 8z) Solving -14 + 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. -14 + 15z + -8z = 8 + 8z + -8z Combine like terms: 15z + -8z = 7z -14 + 7z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -14 + 7z = 8 + 0 -14 + 7z = 8 Add '14' to each side of the equation. -14 + 14 + 7z = 8 + 14 Combine like terms: -14 + 14 = 0 0 + 7z = 8 + 14 7z = 8 + 14 Combine like terms: 8 + 14 = 22 7z = 22 Divide each side by '7'. z = 3.142857143 Simplifying z = 3.142857143
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