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Simplifying -1(5(d + 2) + -6(3d + -2(3d + 8)) + -7) = -18d + 101 Reorder the terms: -1(5(2 + d) + -6(3d + -2(3d + 8)) + -7) = -18d + 101 -1((2 * 5 + d * 5) + -6(3d + -2(3d + 8)) + -7) = -18d + 101 -1((10 + 5d) + -6(3d + -2(3d + 8)) + -7) = -18d + 101 Reorder the terms: -1(10 + 5d + -6(3d + -2(8 + 3d)) + -7) = -18d + 101 -1(10 + 5d + -6(3d + (8 * -2 + 3d * -2)) + -7) = -18d + 101 -1(10 + 5d + -6(3d + (-16 + -6d)) + -7) = -18d + 101 Reorder the terms: -1(10 + 5d + -6(-16 + 3d + -6d) + -7) = -18d + 101 Combine like terms: 3d + -6d = -3d -1(10 + 5d + -6(-16 + -3d) + -7) = -18d + 101 -1(10 + 5d + (-16 * -6 + -3d * -6) + -7) = -18d + 101 -1(10 + 5d + (96 + 18d) + -7) = -18d + 101 Reorder the terms: -1(10 + 96 + -7 + 5d + 18d) = -18d + 101 Combine like terms: 10 + 96 = 106 -1(106 + -7 + 5d + 18d) = -18d + 101 Combine like terms: 106 + -7 = 99 -1(99 + 5d + 18d) = -18d + 101 Combine like terms: 5d + 18d = 23d -1(99 + 23d) = -18d + 101 (99 * -1 + 23d * -1) = -18d + 101 (-99 + -23d) = -18d + 101 Reorder the terms: -99 + -23d = 101 + -18d Solving -99 + -23d = 101 + -18d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '18d' to each side of the equation. -99 + -23d + 18d = 101 + -18d + 18d Combine like terms: -23d + 18d = -5d -99 + -5d = 101 + -18d + 18d Combine like terms: -18d + 18d = 0 -99 + -5d = 101 + 0 -99 + -5d = 101 Add '99' to each side of the equation. -99 + 99 + -5d = 101 + 99 Combine like terms: -99 + 99 = 0 0 + -5d = 101 + 99 -5d = 101 + 99 Combine like terms: 101 + 99 = 200 -5d = 200 Divide each side by '-5'. d = -40 Simplifying d = -40
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