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Simplifying 3(4d + 1) + -9d = 6(2 + -1d) Reorder the terms: 3(1 + 4d) + -9d = 6(2 + -1d) (1 * 3 + 4d * 3) + -9d = 6(2 + -1d) (3 + 12d) + -9d = 6(2 + -1d) Combine like terms: 12d + -9d = 3d 3 + 3d = 6(2 + -1d) 3 + 3d = (2 * 6 + -1d * 6) 3 + 3d = (12 + -6d) Solving 3 + 3d = 12 + -6d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6d' to each side of the equation. 3 + 3d + 6d = 12 + -6d + 6d Combine like terms: 3d + 6d = 9d 3 + 9d = 12 + -6d + 6d Combine like terms: -6d + 6d = 0 3 + 9d = 12 + 0 3 + 9d = 12 Add '-3' to each side of the equation. 3 + -3 + 9d = 12 + -3 Combine like terms: 3 + -3 = 0 0 + 9d = 12 + -3 9d = 12 + -3 Combine like terms: 12 + -3 = 9 9d = 9 Divide each side by '9'. d = 1 Simplifying d = 1
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