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Simplifying 3(d + -8) + 7 = 5(d + 2) + 1 Reorder the terms: 3(-8 + d) + 7 = 5(d + 2) + 1 (-8 * 3 + d * 3) + 7 = 5(d + 2) + 1 (-24 + 3d) + 7 = 5(d + 2) + 1 Reorder the terms: -24 + 7 + 3d = 5(d + 2) + 1 Combine like terms: -24 + 7 = -17 -17 + 3d = 5(d + 2) + 1 Reorder the terms: -17 + 3d = 5(2 + d) + 1 -17 + 3d = (2 * 5 + d * 5) + 1 -17 + 3d = (10 + 5d) + 1 Reorder the terms: -17 + 3d = 10 + 1 + 5d Combine like terms: 10 + 1 = 11 -17 + 3d = 11 + 5d Solving -17 + 3d = 11 + 5d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5d' to each side of the equation. -17 + 3d + -5d = 11 + 5d + -5d Combine like terms: 3d + -5d = -2d -17 + -2d = 11 + 5d + -5d Combine like terms: 5d + -5d = 0 -17 + -2d = 11 + 0 -17 + -2d = 11 Add '17' to each side of the equation. -17 + 17 + -2d = 11 + 17 Combine like terms: -17 + 17 = 0 0 + -2d = 11 + 17 -2d = 11 + 17 Combine like terms: 11 + 17 = 28 -2d = 28 Divide each side by '-2'. d = -14 Simplifying d = -14
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