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Simplifying 2(12 + -1k) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k) (12 * 2 + -1k * 2) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k) (24 + -2k) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k) Reorder the terms: 24 + -2k + -1(2 + k) = 8(2 + -3k) + -3(5 + -6k) 24 + -2k + (2 * -1 + k * -1) = 8(2 + -3k) + -3(5 + -6k) 24 + -2k + (-2 + -1k) = 8(2 + -3k) + -3(5 + -6k) Reorder the terms: 24 + -2 + -2k + -1k = 8(2 + -3k) + -3(5 + -6k) Combine like terms: 24 + -2 = 22 22 + -2k + -1k = 8(2 + -3k) + -3(5 + -6k) Combine like terms: -2k + -1k = -3k 22 + -3k = 8(2 + -3k) + -3(5 + -6k) 22 + -3k = (2 * 8 + -3k * 8) + -3(5 + -6k) 22 + -3k = (16 + -24k) + -3(5 + -6k) 22 + -3k = 16 + -24k + (5 * -3 + -6k * -3) 22 + -3k = 16 + -24k + (-15 + 18k) Reorder the terms: 22 + -3k = 16 + -15 + -24k + 18k Combine like terms: 16 + -15 = 1 22 + -3k = 1 + -24k + 18k Combine like terms: -24k + 18k = -6k 22 + -3k = 1 + -6k Solving 22 + -3k = 1 + -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. 22 + -3k + 6k = 1 + -6k + 6k Combine like terms: -3k + 6k = 3k 22 + 3k = 1 + -6k + 6k Combine like terms: -6k + 6k = 0 22 + 3k = 1 + 0 22 + 3k = 1 Add '-22' to each side of the equation. 22 + -22 + 3k = 1 + -22 Combine like terms: 22 + -22 = 0 0 + 3k = 1 + -22 3k = 1 + -22 Combine like terms: 1 + -22 = -21 3k = -21 Divide each side by '3'. k = -7 Simplifying k = -7
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