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Simplifying 3d + -4(5d + 6) + -1(d + -7) = 4d + 5 Reorder the terms: 3d + -4(6 + 5d) + -1(d + -7) = 4d + 5 3d + (6 * -4 + 5d * -4) + -1(d + -7) = 4d + 5 3d + (-24 + -20d) + -1(d + -7) = 4d + 5 Reorder the terms: 3d + -24 + -20d + -1(-7 + d) = 4d + 5 3d + -24 + -20d + (-7 * -1 + d * -1) = 4d + 5 3d + -24 + -20d + (7 + -1d) = 4d + 5 Reorder the terms: -24 + 7 + 3d + -20d + -1d = 4d + 5 Combine like terms: -24 + 7 = -17 -17 + 3d + -20d + -1d = 4d + 5 Combine like terms: 3d + -20d = -17d -17 + -17d + -1d = 4d + 5 Combine like terms: -17d + -1d = -18d -17 + -18d = 4d + 5 Reorder the terms: -17 + -18d = 5 + 4d Solving -17 + -18d = 5 + 4d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4d' to each side of the equation. -17 + -18d + -4d = 5 + 4d + -4d Combine like terms: -18d + -4d = -22d -17 + -22d = 5 + 4d + -4d Combine like terms: 4d + -4d = 0 -17 + -22d = 5 + 0 -17 + -22d = 5 Add '17' to each side of the equation. -17 + 17 + -22d = 5 + 17 Combine like terms: -17 + 17 = 0 0 + -22d = 5 + 17 -22d = 5 + 17 Combine like terms: 5 + 17 = 22 -22d = 22 Divide each side by '-22'. d = -1 Simplifying d = -1
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