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Simplifying 4k + 5k + 7 + -9k + 3 = 6 + 8k + -5k + -14 + 8 Reorder the terms: 7 + 3 + 4k + 5k + -9k = 6 + 8k + -5k + -14 + 8 Combine like terms: 7 + 3 = 10 10 + 4k + 5k + -9k = 6 + 8k + -5k + -14 + 8 Combine like terms: 4k + 5k = 9k 10 + 9k + -9k = 6 + 8k + -5k + -14 + 8 Combine like terms: 9k + -9k = 0 10 + 0 = 6 + 8k + -5k + -14 + 8 10 = 6 + 8k + -5k + -14 + 8 Reorder the terms: 10 = 6 + -14 + 8 + 8k + -5k Combine like terms: 6 + -14 = -8 10 = -8 + 8 + 8k + -5k Combine like terms: -8 + 8 = 0 10 = 0 + 8k + -5k 10 = 8k + -5k Combine like terms: 8k + -5k = 3k 10 = 3k Solving 10 = 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 10 + -3k = 3k + -3k Combine like terms: 3k + -3k = 0 10 + -3k = 0 Add '-10' to each side of the equation. 10 + -10 + -3k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3k = 0 + -10 -3k = 0 + -10 Combine like terms: 0 + -10 = -10 -3k = -10 Divide each side by '-3'. k = 3.333333333 Simplifying k = 3.333333333
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