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Simplifying 3[d + -8] + -5 = 9[d + 2] + 1 Reorder the terms: 3[-8 + d] + -5 = 9[d + 2] + 1 [-8 * 3 + d * 3] + -5 = 9[d + 2] + 1 [-24 + 3d] + -5 = 9[d + 2] + 1 Reorder the terms: -24 + -5 + 3d = 9[d + 2] + 1 Combine like terms: -24 + -5 = -29 -29 + 3d = 9[d + 2] + 1 Reorder the terms: -29 + 3d = 9[2 + d] + 1 -29 + 3d = [2 * 9 + d * 9] + 1 -29 + 3d = [18 + 9d] + 1 Reorder the terms: -29 + 3d = 18 + 1 + 9d Combine like terms: 18 + 1 = 19 -29 + 3d = 19 + 9d Solving -29 + 3d = 19 + 9d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-9d' to each side of the equation. -29 + 3d + -9d = 19 + 9d + -9d Combine like terms: 3d + -9d = -6d -29 + -6d = 19 + 9d + -9d Combine like terms: 9d + -9d = 0 -29 + -6d = 19 + 0 -29 + -6d = 19 Add '29' to each side of the equation. -29 + 29 + -6d = 19 + 29 Combine like terms: -29 + 29 = 0 0 + -6d = 19 + 29 -6d = 19 + 29 Combine like terms: 19 + 29 = 48 -6d = 48 Divide each side by '-6'. d = -8 Simplifying d = -8
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