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Simplifying 3k + 1 + -5k = 9k + 12 + -8k Reorder the terms: 1 + 3k + -5k = 9k + 12 + -8k Combine like terms: 3k + -5k = -2k 1 + -2k = 9k + 12 + -8k Reorder the terms: 1 + -2k = 12 + 9k + -8k Combine like terms: 9k + -8k = 1k 1 + -2k = 12 + 1k Solving 1 + -2k = 12 + 1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1k' to each side of the equation. 1 + -2k + -1k = 12 + 1k + -1k Combine like terms: -2k + -1k = -3k 1 + -3k = 12 + 1k + -1k Combine like terms: 1k + -1k = 0 1 + -3k = 12 + 0 1 + -3k = 12 Add '-1' to each side of the equation. 1 + -1 + -3k = 12 + -1 Combine like terms: 1 + -1 = 0 0 + -3k = 12 + -1 -3k = 12 + -1 Combine like terms: 12 + -1 = 11 -3k = 11 Divide each side by '-3'. k = -3.666666667 Simplifying k = -3.666666667
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