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Simplifying 9d + 5(8 + d) + -6(2d + -7) = 40 9d + (8 * 5 + d * 5) + -6(2d + -7) = 40 9d + (40 + 5d) + -6(2d + -7) = 40 Reorder the terms: 9d + 40 + 5d + -6(-7 + 2d) = 40 9d + 40 + 5d + (-7 * -6 + 2d * -6) = 40 9d + 40 + 5d + (42 + -12d) = 40 Reorder the terms: 40 + 42 + 9d + 5d + -12d = 40 Combine like terms: 40 + 42 = 82 82 + 9d + 5d + -12d = 40 Combine like terms: 9d + 5d = 14d 82 + 14d + -12d = 40 Combine like terms: 14d + -12d = 2d 82 + 2d = 40 Solving 82 + 2d = 40 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-82' to each side of the equation. 82 + -82 + 2d = 40 + -82 Combine like terms: 82 + -82 = 0 0 + 2d = 40 + -82 2d = 40 + -82 Combine like terms: 40 + -82 = -42 2d = -42 Divide each side by '2'. d = -21 Simplifying d = -21
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