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Simplifying 2(2d + 1) + -3d = 5(3d + -2) + 4d Reorder the terms: 2(1 + 2d) + -3d = 5(3d + -2) + 4d (1 * 2 + 2d * 2) + -3d = 5(3d + -2) + 4d (2 + 4d) + -3d = 5(3d + -2) + 4d Combine like terms: 4d + -3d = 1d 2 + 1d = 5(3d + -2) + 4d Reorder the terms: 2 + 1d = 5(-2 + 3d) + 4d 2 + 1d = (-2 * 5 + 3d * 5) + 4d 2 + 1d = (-10 + 15d) + 4d Combine like terms: 15d + 4d = 19d 2 + 1d = -10 + 19d Solving 2 + 1d = -10 + 19d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-19d' to each side of the equation. 2 + 1d + -19d = -10 + 19d + -19d Combine like terms: 1d + -19d = -18d 2 + -18d = -10 + 19d + -19d Combine like terms: 19d + -19d = 0 2 + -18d = -10 + 0 2 + -18d = -10 Add '-2' to each side of the equation. 2 + -2 + -18d = -10 + -2 Combine like terms: 2 + -2 = 0 0 + -18d = -10 + -2 -18d = -10 + -2 Combine like terms: -10 + -2 = -12 -18d = -12 Divide each side by '-18'. d = 0.6666666667 Simplifying d = 0.6666666667
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