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Simplifying 6(4z + -1) + -4(2 + 8) = 3(z + 1) Reorder the terms: 6(-1 + 4z) + -4(2 + 8) = 3(z + 1) (-1 * 6 + 4z * 6) + -4(2 + 8) = 3(z + 1) (-6 + 24z) + -4(2 + 8) = 3(z + 1) Combine like terms: 2 + 8 = 10 -6 + 24z + -4(10) = 3(z + 1) Multiply -4 * 10 -6 + 24z + -40 = 3(z + 1) Reorder the terms: -6 + -40 + 24z = 3(z + 1) Combine like terms: -6 + -40 = -46 -46 + 24z = 3(z + 1) Reorder the terms: -46 + 24z = 3(1 + z) -46 + 24z = (1 * 3 + z * 3) -46 + 24z = (3 + 3z) Solving -46 + 24z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -46 + 24z + -3z = 3 + 3z + -3z Combine like terms: 24z + -3z = 21z -46 + 21z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -46 + 21z = 3 + 0 -46 + 21z = 3 Add '46' to each side of the equation. -46 + 46 + 21z = 3 + 46 Combine like terms: -46 + 46 = 0 0 + 21z = 3 + 46 21z = 3 + 46 Combine like terms: 3 + 46 = 49 21z = 49 Divide each side by '21'. z = 2.333333333 Simplifying z = 2.333333333
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