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Simplifying 2(3d + 1) + -9d = 8(5 + 2d) Reorder the terms: 2(1 + 3d) + -9d = 8(5 + 2d) (1 * 2 + 3d * 2) + -9d = 8(5 + 2d) (2 + 6d) + -9d = 8(5 + 2d) Combine like terms: 6d + -9d = -3d 2 + -3d = 8(5 + 2d) 2 + -3d = (5 * 8 + 2d * 8) 2 + -3d = (40 + 16d) Solving 2 + -3d = 40 + 16d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-16d' to each side of the equation. 2 + -3d + -16d = 40 + 16d + -16d Combine like terms: -3d + -16d = -19d 2 + -19d = 40 + 16d + -16d Combine like terms: 16d + -16d = 0 2 + -19d = 40 + 0 2 + -19d = 40 Add '-2' to each side of the equation. 2 + -2 + -19d = 40 + -2 Combine like terms: 2 + -2 = 0 0 + -19d = 40 + -2 -19d = 40 + -2 Combine like terms: 40 + -2 = 38 -19d = 38 Divide each side by '-19'. d = -2 Simplifying d = -2
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