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Simplifying 3(4z + -1) + -3(z + 9) = 5(z + 1) Reorder the terms: 3(-1 + 4z) + -3(z + 9) = 5(z + 1) (-1 * 3 + 4z * 3) + -3(z + 9) = 5(z + 1) (-3 + 12z) + -3(z + 9) = 5(z + 1) Reorder the terms: -3 + 12z + -3(9 + z) = 5(z + 1) -3 + 12z + (9 * -3 + z * -3) = 5(z + 1) -3 + 12z + (-27 + -3z) = 5(z + 1) Reorder the terms: -3 + -27 + 12z + -3z = 5(z + 1) Combine like terms: -3 + -27 = -30 -30 + 12z + -3z = 5(z + 1) Combine like terms: 12z + -3z = 9z -30 + 9z = 5(z + 1) Reorder the terms: -30 + 9z = 5(1 + z) -30 + 9z = (1 * 5 + z * 5) -30 + 9z = (5 + 5z) Solving -30 + 9z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -30 + 9z + -5z = 5 + 5z + -5z Combine like terms: 9z + -5z = 4z -30 + 4z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -30 + 4z = 5 + 0 -30 + 4z = 5 Add '30' to each side of the equation. -30 + 30 + 4z = 5 + 30 Combine like terms: -30 + 30 = 0 0 + 4z = 5 + 30 4z = 5 + 30 Combine like terms: 5 + 30 = 35 4z = 35 Divide each side by '4'. z = 8.75 Simplifying z = 8.75
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