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Simplifying 2(d + 1) + 7 = 3(d + -2) + 2d Reorder the terms: 2(1 + d) + 7 = 3(d + -2) + 2d (1 * 2 + d * 2) + 7 = 3(d + -2) + 2d (2 + 2d) + 7 = 3(d + -2) + 2d Reorder the terms: 2 + 7 + 2d = 3(d + -2) + 2d Combine like terms: 2 + 7 = 9 9 + 2d = 3(d + -2) + 2d Reorder the terms: 9 + 2d = 3(-2 + d) + 2d 9 + 2d = (-2 * 3 + d * 3) + 2d 9 + 2d = (-6 + 3d) + 2d Combine like terms: 3d + 2d = 5d 9 + 2d = -6 + 5d Solving 9 + 2d = -6 + 5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5d' to each side of the equation. 9 + 2d + -5d = -6 + 5d + -5d Combine like terms: 2d + -5d = -3d 9 + -3d = -6 + 5d + -5d Combine like terms: 5d + -5d = 0 9 + -3d = -6 + 0 9 + -3d = -6 Add '-9' to each side of the equation. 9 + -9 + -3d = -6 + -9 Combine like terms: 9 + -9 = 0 0 + -3d = -6 + -9 -3d = -6 + -9 Combine like terms: -6 + -9 = -15 -3d = -15 Divide each side by '-3'. d = 5 Simplifying d = 5
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