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Simplifying 6(2z + -1) + -3(z + 8) = 2(z + 1) Reorder the terms: 6(-1 + 2z) + -3(z + 8) = 2(z + 1) (-1 * 6 + 2z * 6) + -3(z + 8) = 2(z + 1) (-6 + 12z) + -3(z + 8) = 2(z + 1) Reorder the terms: -6 + 12z + -3(8 + z) = 2(z + 1) -6 + 12z + (8 * -3 + z * -3) = 2(z + 1) -6 + 12z + (-24 + -3z) = 2(z + 1) Reorder the terms: -6 + -24 + 12z + -3z = 2(z + 1) Combine like terms: -6 + -24 = -30 -30 + 12z + -3z = 2(z + 1) Combine like terms: 12z + -3z = 9z -30 + 9z = 2(z + 1) Reorder the terms: -30 + 9z = 2(1 + z) -30 + 9z = (1 * 2 + z * 2) -30 + 9z = (2 + 2z) Solving -30 + 9z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -30 + 9z + -2z = 2 + 2z + -2z Combine like terms: 9z + -2z = 7z -30 + 7z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -30 + 7z = 2 + 0 -30 + 7z = 2 Add '30' to each side of the equation. -30 + 30 + 7z = 2 + 30 Combine like terms: -30 + 30 = 0 0 + 7z = 2 + 30 7z = 2 + 30 Combine like terms: 2 + 30 = 32 7z = 32 Divide each side by '7'. z = 4.571428571 Simplifying z = 4.571428571
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