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Simplifying k(1 + 2a + 3b) = 0 (1 * k + 2a * k + 3b * k) = 0 Reorder the terms: (2ak + 3bk + 1k) = 0 (2ak + 3bk + 1k) = 0 Solving 2ak + 3bk + 1k = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3bk' to each side of the equation. 2ak + 3bk + -3bk + 1k = 0 + -3bk Combine like terms: 3bk + -3bk = 0 2ak + 0 + 1k = 0 + -3bk 2ak + 1k = 0 + -3bk Remove the zero: 2ak + 1k = -3bk Add '-1k' to each side of the equation. 2ak + 1k + -1k = -3bk + -1k Combine like terms: 1k + -1k = 0 2ak + 0 = -3bk + -1k 2ak = -3bk + -1k Divide each side by '2k'. a = -1.5b + -0.5 Simplifying a = -1.5b + -0.5 Reorder the terms: a = -0.5 + -1.5b
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