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Simplifying 9(k + 1) + -1(8 + 7k) = k Reorder the terms: 9(1 + k) + -1(8 + 7k) = k (1 * 9 + k * 9) + -1(8 + 7k) = k (9 + 9k) + -1(8 + 7k) = k 9 + 9k + (8 * -1 + 7k * -1) = k 9 + 9k + (-8 + -7k) = k Reorder the terms: 9 + -8 + 9k + -7k = k Combine like terms: 9 + -8 = 1 1 + 9k + -7k = k Combine like terms: 9k + -7k = 2k 1 + 2k = k Solving 1 + 2k = k 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 = k + -1k Combine like terms: 2k + -1k = 1k 1 + 1k = k + -1k Combine like terms: k + -1k = 0 1 + 1k = 0 Add '-1' to each side of the equation. 1 + -1 + 1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1k = 0 + -1 1k = 0 + -1 Combine like terms: 0 + -1 = -1 1k = -1 Divide each side by '1'. k = -1 Simplifying k = -1
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