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Simplifying 92 + 2(-28d + 100) = 2(-29d + 78) Reorder the terms: 92 + 2(100 + -28d) = 2(-29d + 78) 92 + (100 * 2 + -28d * 2) = 2(-29d + 78) 92 + (200 + -56d) = 2(-29d + 78) Combine like terms: 92 + 200 = 292 292 + -56d = 2(-29d + 78) Reorder the terms: 292 + -56d = 2(78 + -29d) 292 + -56d = (78 * 2 + -29d * 2) 292 + -56d = (156 + -58d) Solving 292 + -56d = 156 + -58d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '58d' to each side of the equation. 292 + -56d + 58d = 156 + -58d + 58d Combine like terms: -56d + 58d = 2d 292 + 2d = 156 + -58d + 58d Combine like terms: -58d + 58d = 0 292 + 2d = 156 + 0 292 + 2d = 156 Add '-292' to each side of the equation. 292 + -292 + 2d = 156 + -292 Combine like terms: 292 + -292 = 0 0 + 2d = 156 + -292 2d = 156 + -292 Combine like terms: 156 + -292 = -136 2d = -136 Divide each side by '2'. d = -68 Simplifying d = -68
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