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Simplifying 30d + -1(-1d + 6) + (-5 + 4) = -1(5d + 6) + (-8 + 3d) Reorder the terms: 30d + -1(6 + -1d) + (-5 + 4) = -1(5d + 6) + (-8 + 3d) 30d + (6 * -1 + -1d * -1) + (-5 + 4) = -1(5d + 6) + (-8 + 3d) 30d + (-6 + 1d) + (-5 + 4) = -1(5d + 6) + (-8 + 3d) Combine like terms: -5 + 4 = -1 30d + -6 + 1d + (-1) = -1(5d + 6) + (-8 + 3d) 30d + -6 + 1d + -1 = -1(5d + 6) + (-8 + 3d) Reorder the terms: -6 + -1 + 30d + 1d = -1(5d + 6) + (-8 + 3d) Combine like terms: -6 + -1 = -7 -7 + 30d + 1d = -1(5d + 6) + (-8 + 3d) Combine like terms: 30d + 1d = 31d -7 + 31d = -1(5d + 6) + (-8 + 3d) Reorder the terms: -7 + 31d = -1(6 + 5d) + (-8 + 3d) -7 + 31d = (6 * -1 + 5d * -1) + (-8 + 3d) -7 + 31d = (-6 + -5d) + (-8 + 3d) Remove parenthesis around (-8 + 3d) -7 + 31d = -6 + -5d + -8 + 3d Reorder the terms: -7 + 31d = -6 + -8 + -5d + 3d Combine like terms: -6 + -8 = -14 -7 + 31d = -14 + -5d + 3d Combine like terms: -5d + 3d = -2d -7 + 31d = -14 + -2d Solving -7 + 31d = -14 + -2d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2d' to each side of the equation. -7 + 31d + 2d = -14 + -2d + 2d Combine like terms: 31d + 2d = 33d -7 + 33d = -14 + -2d + 2d Combine like terms: -2d + 2d = 0 -7 + 33d = -14 + 0 -7 + 33d = -14 Add '7' to each side of the equation. -7 + 7 + 33d = -14 + 7 Combine like terms: -7 + 7 = 0 0 + 33d = -14 + 7 33d = -14 + 7 Combine like terms: -14 + 7 = -7 33d = -7 Divide each side by '33'. d = -0.2121212121 Simplifying d = -0.2121212121
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