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Simplifying 3(4d + 1) + -9b = 6(2 + -1d) Reorder the terms: 3(1 + 4d) + -9b = 6(2 + -1d) (1 * 3 + 4d * 3) + -9b = 6(2 + -1d) (3 + 12d) + -9b = 6(2 + -1d) Reorder the terms: 3 + -9b + 12d = 6(2 + -1d) 3 + -9b + 12d = (2 * 6 + -1d * 6) 3 + -9b + 12d = (12 + -6d) Solving 3 + -9b + 12d = 12 + -6d Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -9b + -3 + 12d = 12 + -3 + -6d Reorder the terms: 3 + -3 + -9b + 12d = 12 + -3 + -6d Combine like terms: 3 + -3 = 0 0 + -9b + 12d = 12 + -3 + -6d -9b + 12d = 12 + -3 + -6d Combine like terms: 12 + -3 = 9 -9b + 12d = 9 + -6d Add '-12d' to each side of the equation. -9b + 12d + -12d = 9 + -6d + -12d Combine like terms: 12d + -12d = 0 -9b + 0 = 9 + -6d + -12d -9b = 9 + -6d + -12d Combine like terms: -6d + -12d = -18d -9b = 9 + -18d Divide each side by '-9'. b = -1 + 2d Simplifying b = -1 + 2d
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