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Simplifying 3[7 + -1(3d + 6)] + 1 = 7 + -4(2d + 1) + -2d Reorder the terms: 3[7 + -1(6 + 3d)] + 1 = 7 + -4(2d + 1) + -2d 3[7 + (6 * -1 + 3d * -1)] + 1 = 7 + -4(2d + 1) + -2d 3[7 + (-6 + -3d)] + 1 = 7 + -4(2d + 1) + -2d Combine like terms: 7 + -6 = 1 3[1 + -3d] + 1 = 7 + -4(2d + 1) + -2d [1 * 3 + -3d * 3] + 1 = 7 + -4(2d + 1) + -2d [3 + -9d] + 1 = 7 + -4(2d + 1) + -2d Reorder the terms: 3 + 1 + -9d = 7 + -4(2d + 1) + -2d Combine like terms: 3 + 1 = 4 4 + -9d = 7 + -4(2d + 1) + -2d Reorder the terms: 4 + -9d = 7 + -4(1 + 2d) + -2d 4 + -9d = 7 + (1 * -4 + 2d * -4) + -2d 4 + -9d = 7 + (-4 + -8d) + -2d Combine like terms: 7 + -4 = 3 4 + -9d = 3 + -8d + -2d Combine like terms: -8d + -2d = -10d 4 + -9d = 3 + -10d Solving 4 + -9d = 3 + -10d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10d' to each side of the equation. 4 + -9d + 10d = 3 + -10d + 10d Combine like terms: -9d + 10d = 1d 4 + 1d = 3 + -10d + 10d Combine like terms: -10d + 10d = 0 4 + 1d = 3 + 0 4 + 1d = 3 Add '-4' to each side of the equation. 4 + -4 + 1d = 3 + -4 Combine like terms: 4 + -4 = 0 0 + 1d = 3 + -4 1d = 3 + -4 Combine like terms: 3 + -4 = -1 1d = -1 Divide each side by '1'. d = -1 Simplifying d = -1
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