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Simplifying 6(k + 9) + -1(5k + -2) = 1 Reorder the terms: 6(9 + k) + -1(5k + -2) = 1 (9 * 6 + k * 6) + -1(5k + -2) = 1 (54 + 6k) + -1(5k + -2) = 1 Reorder the terms: 54 + 6k + -1(-2 + 5k) = 1 54 + 6k + (-2 * -1 + 5k * -1) = 1 54 + 6k + (2 + -5k) = 1 Reorder the terms: 54 + 2 + 6k + -5k = 1 Combine like terms: 54 + 2 = 56 56 + 6k + -5k = 1 Combine like terms: 6k + -5k = 1k 56 + 1k = 1 Solving 56 + 1k = 1 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-56' to each side of the equation. 56 + -56 + 1k = 1 + -56 Combine like terms: 56 + -56 = 0 0 + 1k = 1 + -56 1k = 1 + -56 Combine like terms: 1 + -56 = -55 1k = -55 Divide each side by '1'. k = -55 Simplifying k = -55
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