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Simplifying 2(d + 3) + 5(d + 5) = 45 Reorder the terms: 2(3 + d) + 5(d + 5) = 45 (3 * 2 + d * 2) + 5(d + 5) = 45 (6 + 2d) + 5(d + 5) = 45 Reorder the terms: 6 + 2d + 5(5 + d) = 45 6 + 2d + (5 * 5 + d * 5) = 45 6 + 2d + (25 + 5d) = 45 Reorder the terms: 6 + 25 + 2d + 5d = 45 Combine like terms: 6 + 25 = 31 31 + 2d + 5d = 45 Combine like terms: 2d + 5d = 7d 31 + 7d = 45 Solving 31 + 7d = 45 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + 7d = 45 + -31 Combine like terms: 31 + -31 = 0 0 + 7d = 45 + -31 7d = 45 + -31 Combine like terms: 45 + -31 = 14 7d = 14 Divide each side by '7'. d = 2 Simplifying d = 2
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