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Simplifying 6(5z + -1) + -3(z + 6) = 22(z + 1) Reorder the terms: 6(-1 + 5z) + -3(z + 6) = 22(z + 1) (-1 * 6 + 5z * 6) + -3(z + 6) = 22(z + 1) (-6 + 30z) + -3(z + 6) = 22(z + 1) Reorder the terms: -6 + 30z + -3(6 + z) = 22(z + 1) -6 + 30z + (6 * -3 + z * -3) = 22(z + 1) -6 + 30z + (-18 + -3z) = 22(z + 1) Reorder the terms: -6 + -18 + 30z + -3z = 22(z + 1) Combine like terms: -6 + -18 = -24 -24 + 30z + -3z = 22(z + 1) Combine like terms: 30z + -3z = 27z -24 + 27z = 22(z + 1) Reorder the terms: -24 + 27z = 22(1 + z) -24 + 27z = (1 * 22 + z * 22) -24 + 27z = (22 + 22z) Solving -24 + 27z = 22 + 22z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-22z' to each side of the equation. -24 + 27z + -22z = 22 + 22z + -22z Combine like terms: 27z + -22z = 5z -24 + 5z = 22 + 22z + -22z Combine like terms: 22z + -22z = 0 -24 + 5z = 22 + 0 -24 + 5z = 22 Add '24' to each side of the equation. -24 + 24 + 5z = 22 + 24 Combine like terms: -24 + 24 = 0 0 + 5z = 22 + 24 5z = 22 + 24 Combine like terms: 22 + 24 = 46 5z = 46 Divide each side by '5'. z = 9.2 Simplifying z = 9.2
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