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Simplifying (1 + -2k + -3k) + (2 + 4k + 5k) = 0 Combine like terms: -2k + -3k = -5k (1 + -5k) + (2 + 4k + 5k) = 0 Remove parenthesis around (1 + -5k) 1 + -5k + (2 + 4k + 5k) = 0 Combine like terms: 4k + 5k = 9k 1 + -5k + (2 + 9k) = 0 Remove parenthesis around (2 + 9k) 1 + -5k + 2 + 9k = 0 Reorder the terms: 1 + 2 + -5k + 9k = 0 Combine like terms: 1 + 2 = 3 3 + -5k + 9k = 0 Combine like terms: -5k + 9k = 4k 3 + 4k = 0 Solving 3 + 4k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4k = 0 + -3 4k = 0 + -3 Combine like terms: 0 + -3 = -3 4k = -3 Divide each side by '4'. k = -0.75 Simplifying k = -0.75
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