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Simplifying 7 + -2(2d + -1) + -13(d + 1) = 59 + -8d Reorder the terms: 7 + -2(-1 + 2d) + -13(d + 1) = 59 + -8d 7 + (-1 * -2 + 2d * -2) + -13(d + 1) = 59 + -8d 7 + (2 + -4d) + -13(d + 1) = 59 + -8d Reorder the terms: 7 + 2 + -4d + -13(1 + d) = 59 + -8d 7 + 2 + -4d + (1 * -13 + d * -13) = 59 + -8d 7 + 2 + -4d + (-13 + -13d) = 59 + -8d Reorder the terms: 7 + 2 + -13 + -4d + -13d = 59 + -8d Combine like terms: 7 + 2 = 9 9 + -13 + -4d + -13d = 59 + -8d Combine like terms: 9 + -13 = -4 -4 + -4d + -13d = 59 + -8d Combine like terms: -4d + -13d = -17d -4 + -17d = 59 + -8d Solving -4 + -17d = 59 + -8d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '8d' to each side of the equation. -4 + -17d + 8d = 59 + -8d + 8d Combine like terms: -17d + 8d = -9d -4 + -9d = 59 + -8d + 8d Combine like terms: -8d + 8d = 0 -4 + -9d = 59 + 0 -4 + -9d = 59 Add '4' to each side of the equation. -4 + 4 + -9d = 59 + 4 Combine like terms: -4 + 4 = 0 0 + -9d = 59 + 4 -9d = 59 + 4 Combine like terms: 59 + 4 = 63 -9d = 63 Divide each side by '-9'. d = -7 Simplifying d = -7
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