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Simplifying 3.2 = 2.5(3d + 5) + 3(2d + 5) Reorder the terms: 3.2 = 2.5(5 + 3d) + 3(2d + 5) 3.2 = (5 * 2.5 + 3d * 2.5) + 3(2d + 5) 3.2 = (12.5 + 7.5d) + 3(2d + 5) Reorder the terms: 3.2 = 12.5 + 7.5d + 3(5 + 2d) 3.2 = 12.5 + 7.5d + (5 * 3 + 2d * 3) 3.2 = 12.5 + 7.5d + (15 + 6d) Reorder the terms: 3.2 = 12.5 + 15 + 7.5d + 6d Combine like terms: 12.5 + 15 = 27.5 3.2 = 27.5 + 7.5d + 6d Combine like terms: 7.5d + 6d = 13.5d 3.2 = 27.5 + 13.5d Solving 3.2 = 27.5 + 13.5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-13.5d' to each side of the equation. 3.2 + -13.5d = 27.5 + 13.5d + -13.5d Combine like terms: 13.5d + -13.5d = 0.0 3.2 + -13.5d = 27.5 + 0.0 3.2 + -13.5d = 27.5 Add '-3.2' to each side of the equation. 3.2 + -3.2 + -13.5d = 27.5 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -13.5d = 27.5 + -3.2 -13.5d = 27.5 + -3.2 Combine like terms: 27.5 + -3.2 = 24.3 -13.5d = 24.3 Divide each side by '-13.5'. d = -1.8 Simplifying d = -1.8
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