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Simplifying 3(1 + -1k) = -2(5k + 1) + 8k (1 * 3 + -1k * 3) = -2(5k + 1) + 8k (3 + -3k) = -2(5k + 1) + 8k Reorder the terms: 3 + -3k = -2(1 + 5k) + 8k 3 + -3k = (1 * -2 + 5k * -2) + 8k 3 + -3k = (-2 + -10k) + 8k Combine like terms: -10k + 8k = -2k 3 + -3k = -2 + -2k Solving 3 + -3k = -2 + -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. 3 + -3k + 2k = -2 + -2k + 2k Combine like terms: -3k + 2k = -1k 3 + -1k = -2 + -2k + 2k Combine like terms: -2k + 2k = 0 3 + -1k = -2 + 0 3 + -1k = -2 Add '-3' to each side of the equation. 3 + -3 + -1k = -2 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = -2 + -3 -1k = -2 + -3 Combine like terms: -2 + -3 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5
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