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Simplifying 2[d + -1(4d + 19) + 9] = 2(d + 10) Reorder the terms: 2[d + -1(19 + 4d) + 9] = 2(d + 10) 2[d + (19 * -1 + 4d * -1) + 9] = 2(d + 10) 2[d + (-19 + -4d) + 9] = 2(d + 10) Reorder the terms: 2[-19 + 9 + d + -4d] = 2(d + 10) Combine like terms: -19 + 9 = -10 2[-10 + d + -4d] = 2(d + 10) Combine like terms: d + -4d = -3d 2[-10 + -3d] = 2(d + 10) [-10 * 2 + -3d * 2] = 2(d + 10) [-20 + -6d] = 2(d + 10) Reorder the terms: -20 + -6d = 2(10 + d) -20 + -6d = (10 * 2 + d * 2) -20 + -6d = (20 + 2d) Solving -20 + -6d = 20 + 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. -20 + -6d + -2d = 20 + 2d + -2d Combine like terms: -6d + -2d = -8d -20 + -8d = 20 + 2d + -2d Combine like terms: 2d + -2d = 0 -20 + -8d = 20 + 0 -20 + -8d = 20 Add '20' to each side of the equation. -20 + 20 + -8d = 20 + 20 Combine like terms: -20 + 20 = 0 0 + -8d = 20 + 20 -8d = 20 + 20 Combine like terms: 20 + 20 = 40 -8d = 40 Divide each side by '-8'. d = -5 Simplifying d = -5
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