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Simplifying 3(6z + -1) + -3(z + 7) = 8(z + 1) Reorder the terms: 3(-1 + 6z) + -3(z + 7) = 8(z + 1) (-1 * 3 + 6z * 3) + -3(z + 7) = 8(z + 1) (-3 + 18z) + -3(z + 7) = 8(z + 1) Reorder the terms: -3 + 18z + -3(7 + z) = 8(z + 1) -3 + 18z + (7 * -3 + z * -3) = 8(z + 1) -3 + 18z + (-21 + -3z) = 8(z + 1) Reorder the terms: -3 + -21 + 18z + -3z = 8(z + 1) Combine like terms: -3 + -21 = -24 -24 + 18z + -3z = 8(z + 1) Combine like terms: 18z + -3z = 15z -24 + 15z = 8(z + 1) Reorder the terms: -24 + 15z = 8(1 + z) -24 + 15z = (1 * 8 + z * 8) -24 + 15z = (8 + 8z) Solving -24 + 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. -24 + 15z + -8z = 8 + 8z + -8z Combine like terms: 15z + -8z = 7z -24 + 7z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -24 + 7z = 8 + 0 -24 + 7z = 8 Add '24' to each side of the equation. -24 + 24 + 7z = 8 + 24 Combine like terms: -24 + 24 = 0 0 + 7z = 8 + 24 7z = 8 + 24 Combine like terms: 8 + 24 = 32 7z = 32 Divide each side by '7'. z = 4.571428571 Simplifying z = 4.571428571
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