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Simplifying 7(k + 6) + -1(6k + -9) = 9 Reorder the terms: 7(6 + k) + -1(6k + -9) = 9 (6 * 7 + k * 7) + -1(6k + -9) = 9 (42 + 7k) + -1(6k + -9) = 9 Reorder the terms: 42 + 7k + -1(-9 + 6k) = 9 42 + 7k + (-9 * -1 + 6k * -1) = 9 42 + 7k + (9 + -6k) = 9 Reorder the terms: 42 + 9 + 7k + -6k = 9 Combine like terms: 42 + 9 = 51 51 + 7k + -6k = 9 Combine like terms: 7k + -6k = 1k 51 + 1k = 9 Solving 51 + 1k = 9 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-51' to each side of the equation. 51 + -51 + 1k = 9 + -51 Combine like terms: 51 + -51 = 0 0 + 1k = 9 + -51 1k = 9 + -51 Combine like terms: 9 + -51 = -42 1k = -42 Divide each side by '1'. k = -42 Simplifying k = -42
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