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Simplifying (3k + 12 + -1k) * 3 = k + -1(4 + -1k) Reorder the terms: (12 + 3k + -1k) * 3 = k + -1(4 + -1k) Combine like terms: 3k + -1k = 2k (12 + 2k) * 3 = k + -1(4 + -1k) Reorder the terms for easier multiplication: 3(12 + 2k) = k + -1(4 + -1k) (12 * 3 + 2k * 3) = k + -1(4 + -1k) (36 + 6k) = k + -1(4 + -1k) 36 + 6k = k + (4 * -1 + -1k * -1) 36 + 6k = k + (-4 + 1k) Reorder the terms: 36 + 6k = -4 + k + 1k Combine like terms: k + 1k = 2k 36 + 6k = -4 + 2k Solving 36 + 6k = -4 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 36 + 6k + -2k = -4 + 2k + -2k Combine like terms: 6k + -2k = 4k 36 + 4k = -4 + 2k + -2k Combine like terms: 2k + -2k = 0 36 + 4k = -4 + 0 36 + 4k = -4 Add '-36' to each side of the equation. 36 + -36 + 4k = -4 + -36 Combine like terms: 36 + -36 = 0 0 + 4k = -4 + -36 4k = -4 + -36 Combine like terms: -4 + -36 = -40 4k = -40 Divide each side by '4'. k = -10 Simplifying k = -10
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