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Simplifying 5d + 6(d + -7) = 30 + 2d Reorder the terms: 5d + 6(-7 + d) = 30 + 2d 5d + (-7 * 6 + d * 6) = 30 + 2d 5d + (-42 + 6d) = 30 + 2d Reorder the terms: -42 + 5d + 6d = 30 + 2d Combine like terms: 5d + 6d = 11d -42 + 11d = 30 + 2d Solving -42 + 11d = 30 + 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. -42 + 11d + -2d = 30 + 2d + -2d Combine like terms: 11d + -2d = 9d -42 + 9d = 30 + 2d + -2d Combine like terms: 2d + -2d = 0 -42 + 9d = 30 + 0 -42 + 9d = 30 Add '42' to each side of the equation. -42 + 42 + 9d = 30 + 42 Combine like terms: -42 + 42 = 0 0 + 9d = 30 + 42 9d = 30 + 42 Combine like terms: 30 + 42 = 72 9d = 72 Divide each side by '9'. d = 8 Simplifying d = 8
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