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Simplifying 2 + -7(d + -1) = 3(d + -2) + -5(3 + d) Reorder the terms: 2 + -7(-1 + d) = 3(d + -2) + -5(3 + d) 2 + (-1 * -7 + d * -7) = 3(d + -2) + -5(3 + d) 2 + (7 + -7d) = 3(d + -2) + -5(3 + d) Combine like terms: 2 + 7 = 9 9 + -7d = 3(d + -2) + -5(3 + d) Reorder the terms: 9 + -7d = 3(-2 + d) + -5(3 + d) 9 + -7d = (-2 * 3 + d * 3) + -5(3 + d) 9 + -7d = (-6 + 3d) + -5(3 + d) 9 + -7d = -6 + 3d + (3 * -5 + d * -5) 9 + -7d = -6 + 3d + (-15 + -5d) Reorder the terms: 9 + -7d = -6 + -15 + 3d + -5d Combine like terms: -6 + -15 = -21 9 + -7d = -21 + 3d + -5d Combine like terms: 3d + -5d = -2d 9 + -7d = -21 + -2d Solving 9 + -7d = -21 + -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. 9 + -7d + 2d = -21 + -2d + 2d Combine like terms: -7d + 2d = -5d 9 + -5d = -21 + -2d + 2d Combine like terms: -2d + 2d = 0 9 + -5d = -21 + 0 9 + -5d = -21 Add '-9' to each side of the equation. 9 + -9 + -5d = -21 + -9 Combine like terms: 9 + -9 = 0 0 + -5d = -21 + -9 -5d = -21 + -9 Combine like terms: -21 + -9 = -30 -5d = -30 Divide each side by '-5'. d = 6 Simplifying d = 6
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