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Simplifying 4 + -2(d + 7) + -1(3d + 5) = 2d + (4d + -9 + 3d) + -1(d + -3) Reorder the terms: 4 + -2(7 + d) + -1(3d + 5) = 2d + (4d + -9 + 3d) + -1(d + -3) 4 + (7 * -2 + d * -2) + -1(3d + 5) = 2d + (4d + -9 + 3d) + -1(d + -3) 4 + (-14 + -2d) + -1(3d + 5) = 2d + (4d + -9 + 3d) + -1(d + -3) Reorder the terms: 4 + -14 + -2d + -1(5 + 3d) = 2d + (4d + -9 + 3d) + -1(d + -3) 4 + -14 + -2d + (5 * -1 + 3d * -1) = 2d + (4d + -9 + 3d) + -1(d + -3) 4 + -14 + -2d + (-5 + -3d) = 2d + (4d + -9 + 3d) + -1(d + -3) Reorder the terms: 4 + -14 + -5 + -2d + -3d = 2d + (4d + -9 + 3d) + -1(d + -3) Combine like terms: 4 + -14 = -10 -10 + -5 + -2d + -3d = 2d + (4d + -9 + 3d) + -1(d + -3) Combine like terms: -10 + -5 = -15 -15 + -2d + -3d = 2d + (4d + -9 + 3d) + -1(d + -3) Combine like terms: -2d + -3d = -5d -15 + -5d = 2d + (4d + -9 + 3d) + -1(d + -3) Reorder the terms: -15 + -5d = 2d + (-9 + 4d + 3d) + -1(d + -3) Combine like terms: 4d + 3d = 7d -15 + -5d = 2d + (-9 + 7d) + -1(d + -3) Remove parenthesis around (-9 + 7d) -15 + -5d = 2d + -9 + 7d + -1(d + -3) Reorder the terms: -15 + -5d = 2d + -9 + 7d + -1(-3 + d) -15 + -5d = 2d + -9 + 7d + (-3 * -1 + d * -1) -15 + -5d = 2d + -9 + 7d + (3 + -1d) Reorder the terms: -15 + -5d = -9 + 3 + 2d + 7d + -1d Combine like terms: -9 + 3 = -6 -15 + -5d = -6 + 2d + 7d + -1d Combine like terms: 2d + 7d = 9d -15 + -5d = -6 + 9d + -1d Combine like terms: 9d + -1d = 8d -15 + -5d = -6 + 8d Solving -15 + -5d = -6 + 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. -15 + -5d + -8d = -6 + 8d + -8d Combine like terms: -5d + -8d = -13d -15 + -13d = -6 + 8d + -8d Combine like terms: 8d + -8d = 0 -15 + -13d = -6 + 0 -15 + -13d = -6 Add '15' to each side of the equation. -15 + 15 + -13d = -6 + 15 Combine like terms: -15 + 15 = 0 0 + -13d = -6 + 15 -13d = -6 + 15 Combine like terms: -6 + 15 = 9 -13d = 9 Divide each side by '-13'. d = -0.6923076923 Simplifying d = -0.6923076923
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