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Simplifying 6(4z + -1) + -3(z + 6) = 13(z + 1) Reorder the terms: 6(-1 + 4z) + -3(z + 6) = 13(z + 1) (-1 * 6 + 4z * 6) + -3(z + 6) = 13(z + 1) (-6 + 24z) + -3(z + 6) = 13(z + 1) Reorder the terms: -6 + 24z + -3(6 + z) = 13(z + 1) -6 + 24z + (6 * -3 + z * -3) = 13(z + 1) -6 + 24z + (-18 + -3z) = 13(z + 1) Reorder the terms: -6 + -18 + 24z + -3z = 13(z + 1) Combine like terms: -6 + -18 = -24 -24 + 24z + -3z = 13(z + 1) Combine like terms: 24z + -3z = 21z -24 + 21z = 13(z + 1) Reorder the terms: -24 + 21z = 13(1 + z) -24 + 21z = (1 * 13 + z * 13) -24 + 21z = (13 + 13z) Solving -24 + 21z = 13 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. -24 + 21z + -13z = 13 + 13z + -13z Combine like terms: 21z + -13z = 8z -24 + 8z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -24 + 8z = 13 + 0 -24 + 8z = 13 Add '24' to each side of the equation. -24 + 24 + 8z = 13 + 24 Combine like terms: -24 + 24 = 0 0 + 8z = 13 + 24 8z = 13 + 24 Combine like terms: 13 + 24 = 37 8z = 37 Divide each side by '8'. z = 4.625 Simplifying z = 4.625
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