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Simplifying 2[d + -1(2d + 10) + 9] = 2(d + 1) Reorder the terms: 2[d + -1(10 + 2d) + 9] = 2(d + 1) 2[d + (10 * -1 + 2d * -1) + 9] = 2(d + 1) 2[d + (-10 + -2d) + 9] = 2(d + 1) Reorder the terms: 2[-10 + 9 + d + -2d] = 2(d + 1) Combine like terms: -10 + 9 = -1 2[-1 + d + -2d] = 2(d + 1) Combine like terms: d + -2d = -1d 2[-1 + -1d] = 2(d + 1) [-1 * 2 + -1d * 2] = 2(d + 1) [-2 + -2d] = 2(d + 1) Reorder the terms: -2 + -2d = 2(1 + d) -2 + -2d = (1 * 2 + d * 2) -2 + -2d = (2 + 2d) Solving -2 + -2d = 2 + 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. -2 + -2d + -2d = 2 + 2d + -2d Combine like terms: -2d + -2d = -4d -2 + -4d = 2 + 2d + -2d Combine like terms: 2d + -2d = 0 -2 + -4d = 2 + 0 -2 + -4d = 2 Add '2' to each side of the equation. -2 + 2 + -4d = 2 + 2 Combine like terms: -2 + 2 = 0 0 + -4d = 2 + 2 -4d = 2 + 2 Combine like terms: 2 + 2 = 4 -4d = 4 Divide each side by '-4'. d = -1 Simplifying d = -1
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