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Simplifying 2[d + -1(4d + 7) + 5] = 2(d + 2) Reorder the terms: 2[d + -1(7 + 4d) + 5] = 2(d + 2) 2[d + (7 * -1 + 4d * -1) + 5] = 2(d + 2) 2[d + (-7 + -4d) + 5] = 2(d + 2) Reorder the terms: 2[-7 + 5 + d + -4d] = 2(d + 2) Combine like terms: -7 + 5 = -2 2[-2 + d + -4d] = 2(d + 2) Combine like terms: d + -4d = -3d 2[-2 + -3d] = 2(d + 2) [-2 * 2 + -3d * 2] = 2(d + 2) [-4 + -6d] = 2(d + 2) Reorder the terms: -4 + -6d = 2(2 + d) -4 + -6d = (2 * 2 + d * 2) -4 + -6d = (4 + 2d) Solving -4 + -6d = 4 + 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. -4 + -6d + -2d = 4 + 2d + -2d Combine like terms: -6d + -2d = -8d -4 + -8d = 4 + 2d + -2d Combine like terms: 2d + -2d = 0 -4 + -8d = 4 + 0 -4 + -8d = 4 Add '4' to each side of the equation. -4 + 4 + -8d = 4 + 4 Combine like terms: -4 + 4 = 0 0 + -8d = 4 + 4 -8d = 4 + 4 Combine like terms: 4 + 4 = 8 -8d = 8 Divide each side by '-8'. d = -1 Simplifying d = -1
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