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Simplifying 6(5z + -1) + -3(z + 2) = 20(z + 1) Reorder the terms: 6(-1 + 5z) + -3(z + 2) = 20(z + 1) (-1 * 6 + 5z * 6) + -3(z + 2) = 20(z + 1) (-6 + 30z) + -3(z + 2) = 20(z + 1) Reorder the terms: -6 + 30z + -3(2 + z) = 20(z + 1) -6 + 30z + (2 * -3 + z * -3) = 20(z + 1) -6 + 30z + (-6 + -3z) = 20(z + 1) Reorder the terms: -6 + -6 + 30z + -3z = 20(z + 1) Combine like terms: -6 + -6 = -12 -12 + 30z + -3z = 20(z + 1) Combine like terms: 30z + -3z = 27z -12 + 27z = 20(z + 1) Reorder the terms: -12 + 27z = 20(1 + z) -12 + 27z = (1 * 20 + z * 20) -12 + 27z = (20 + 20z) Solving -12 + 27z = 20 + 20z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-20z' to each side of the equation. -12 + 27z + -20z = 20 + 20z + -20z Combine like terms: 27z + -20z = 7z -12 + 7z = 20 + 20z + -20z Combine like terms: 20z + -20z = 0 -12 + 7z = 20 + 0 -12 + 7z = 20 Add '12' to each side of the equation. -12 + 12 + 7z = 20 + 12 Combine like terms: -12 + 12 = 0 0 + 7z = 20 + 12 7z = 20 + 12 Combine like terms: 20 + 12 = 32 7z = 32 Divide each side by '7'. z = 4.571428571 Simplifying z = 4.571428571
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