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Simplifying 3(5d + 1) = 19 + -1(2d + -5) + 14d Reorder the terms: 3(1 + 5d) = 19 + -1(2d + -5) + 14d (1 * 3 + 5d * 3) = 19 + -1(2d + -5) + 14d (3 + 15d) = 19 + -1(2d + -5) + 14d Reorder the terms: 3 + 15d = 19 + -1(-5 + 2d) + 14d 3 + 15d = 19 + (-5 * -1 + 2d * -1) + 14d 3 + 15d = 19 + (5 + -2d) + 14d Combine like terms: 19 + 5 = 24 3 + 15d = 24 + -2d + 14d Combine like terms: -2d + 14d = 12d 3 + 15d = 24 + 12d Solving 3 + 15d = 24 + 12d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12d' to each side of the equation. 3 + 15d + -12d = 24 + 12d + -12d Combine like terms: 15d + -12d = 3d 3 + 3d = 24 + 12d + -12d Combine like terms: 12d + -12d = 0 3 + 3d = 24 + 0 3 + 3d = 24 Add '-3' to each side of the equation. 3 + -3 + 3d = 24 + -3 Combine like terms: 3 + -3 = 0 0 + 3d = 24 + -3 3d = 24 + -3 Combine like terms: 24 + -3 = 21 3d = 21 Divide each side by '3'. d = 7 Simplifying d = 7
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