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Simplifying 3(d + -8) + 7 = 5(d + 2) + -3d + -19 Reorder the terms: 3(-8 + d) + 7 = 5(d + 2) + -3d + -19 (-8 * 3 + d * 3) + 7 = 5(d + 2) + -3d + -19 (-24 + 3d) + 7 = 5(d + 2) + -3d + -19 Reorder the terms: -24 + 7 + 3d = 5(d + 2) + -3d + -19 Combine like terms: -24 + 7 = -17 -17 + 3d = 5(d + 2) + -3d + -19 Reorder the terms: -17 + 3d = 5(2 + d) + -3d + -19 -17 + 3d = (2 * 5 + d * 5) + -3d + -19 -17 + 3d = (10 + 5d) + -3d + -19 Reorder the terms: -17 + 3d = 10 + -19 + 5d + -3d Combine like terms: 10 + -19 = -9 -17 + 3d = -9 + 5d + -3d Combine like terms: 5d + -3d = 2d -17 + 3d = -9 + 2d Solving -17 + 3d = -9 + 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. -17 + 3d + -2d = -9 + 2d + -2d Combine like terms: 3d + -2d = 1d -17 + 1d = -9 + 2d + -2d Combine like terms: 2d + -2d = 0 -17 + 1d = -9 + 0 -17 + 1d = -9 Add '17' to each side of the equation. -17 + 17 + 1d = -9 + 17 Combine like terms: -17 + 17 = 0 0 + 1d = -9 + 17 1d = -9 + 17 Combine like terms: -9 + 17 = 8 1d = 8 Divide each side by '1'. d = 8 Simplifying d = 8
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