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Simplifying -8(k + -2) + -3(1 + -3k) = 2 + 10k + 1 + -8k Reorder the terms: -8(-2 + k) + -3(1 + -3k) = 2 + 10k + 1 + -8k (-2 * -8 + k * -8) + -3(1 + -3k) = 2 + 10k + 1 + -8k (16 + -8k) + -3(1 + -3k) = 2 + 10k + 1 + -8k 16 + -8k + (1 * -3 + -3k * -3) = 2 + 10k + 1 + -8k 16 + -8k + (-3 + 9k) = 2 + 10k + 1 + -8k Reorder the terms: 16 + -3 + -8k + 9k = 2 + 10k + 1 + -8k Combine like terms: 16 + -3 = 13 13 + -8k + 9k = 2 + 10k + 1 + -8k Combine like terms: -8k + 9k = 1k 13 + 1k = 2 + 10k + 1 + -8k Reorder the terms: 13 + 1k = 2 + 1 + 10k + -8k Combine like terms: 2 + 1 = 3 13 + 1k = 3 + 10k + -8k Combine like terms: 10k + -8k = 2k 13 + 1k = 3 + 2k Solving 13 + 1k = 3 + 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. 13 + 1k + -2k = 3 + 2k + -2k Combine like terms: 1k + -2k = -1k 13 + -1k = 3 + 2k + -2k Combine like terms: 2k + -2k = 0 13 + -1k = 3 + 0 13 + -1k = 3 Add '-13' to each side of the equation. 13 + -13 + -1k = 3 + -13 Combine like terms: 13 + -13 = 0 0 + -1k = 3 + -13 -1k = 3 + -13 Combine like terms: 3 + -13 = -10 -1k = -10 Divide each side by '-1'. k = 10 Simplifying k = 10
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