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Simplifying 5(k + 6) + -1(1 + -7k) = 11k Reorder the terms: 5(6 + k) + -1(1 + -7k) = 11k (6 * 5 + k * 5) + -1(1 + -7k) = 11k (30 + 5k) + -1(1 + -7k) = 11k 30 + 5k + (1 * -1 + -7k * -1) = 11k 30 + 5k + (-1 + 7k) = 11k Reorder the terms: 30 + -1 + 5k + 7k = 11k Combine like terms: 30 + -1 = 29 29 + 5k + 7k = 11k Combine like terms: 5k + 7k = 12k 29 + 12k = 11k Solving 29 + 12k = 11k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11k' to each side of the equation. 29 + 12k + -11k = 11k + -11k Combine like terms: 12k + -11k = 1k 29 + 1k = 11k + -11k Combine like terms: 11k + -11k = 0 29 + 1k = 0 Add '-29' to each side of the equation. 29 + -29 + 1k = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 1k = 0 + -29 1k = 0 + -29 Combine like terms: 0 + -29 = -29 1k = -29 Divide each side by '1'. k = -29 Simplifying k = -29
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