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Simplifying -4(d + 1) + 3 = 12 + -1(d + 4) Reorder the terms: -4(1 + d) + 3 = 12 + -1(d + 4) (1 * -4 + d * -4) + 3 = 12 + -1(d + 4) (-4 + -4d) + 3 = 12 + -1(d + 4) Reorder the terms: -4 + 3 + -4d = 12 + -1(d + 4) Combine like terms: -4 + 3 = -1 -1 + -4d = 12 + -1(d + 4) Reorder the terms: -1 + -4d = 12 + -1(4 + d) -1 + -4d = 12 + (4 * -1 + d * -1) -1 + -4d = 12 + (-4 + -1d) Combine like terms: 12 + -4 = 8 -1 + -4d = 8 + -1d Solving -1 + -4d = 8 + -1d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add 'd' to each side of the equation. -1 + -4d + d = 8 + -1d + d Combine like terms: -4d + d = -3d -1 + -3d = 8 + -1d + d Combine like terms: -1d + d = 0 -1 + -3d = 8 + 0 -1 + -3d = 8 Add '1' to each side of the equation. -1 + 1 + -3d = 8 + 1 Combine like terms: -1 + 1 = 0 0 + -3d = 8 + 1 -3d = 8 + 1 Combine like terms: 8 + 1 = 9 -3d = 9 Divide each side by '-3'. d = -3 Simplifying d = -3
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