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Simplifying 7(k + 7) + -1(-6k + -1) = 12k Reorder the terms: 7(7 + k) + -1(-6k + -1) = 12k (7 * 7 + k * 7) + -1(-6k + -1) = 12k (49 + 7k) + -1(-6k + -1) = 12k Reorder the terms: 49 + 7k + -1(-1 + -6k) = 12k 49 + 7k + (-1 * -1 + -6k * -1) = 12k 49 + 7k + (1 + 6k) = 12k Reorder the terms: 49 + 1 + 7k + 6k = 12k Combine like terms: 49 + 1 = 50 50 + 7k + 6k = 12k Combine like terms: 7k + 6k = 13k 50 + 13k = 12k Solving 50 + 13k = 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. 50 + 13k + -12k = 12k + -12k Combine like terms: 13k + -12k = 1k 50 + 1k = 12k + -12k Combine like terms: 12k + -12k = 0 50 + 1k = 0 Add '-50' to each side of the equation. 50 + -50 + 1k = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 1k = 0 + -50 1k = 0 + -50 Combine like terms: 0 + -50 = -50 1k = -50 Divide each side by '1'. k = -50 Simplifying k = -50
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