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Simplifying 2(6k + 2) + -1(7k + 3) = 1 + k + 2k Reorder the terms: 2(2 + 6k) + -1(7k + 3) = 1 + k + 2k (2 * 2 + 6k * 2) + -1(7k + 3) = 1 + k + 2k (4 + 12k) + -1(7k + 3) = 1 + k + 2k Reorder the terms: 4 + 12k + -1(3 + 7k) = 1 + k + 2k 4 + 12k + (3 * -1 + 7k * -1) = 1 + k + 2k 4 + 12k + (-3 + -7k) = 1 + k + 2k Reorder the terms: 4 + -3 + 12k + -7k = 1 + k + 2k Combine like terms: 4 + -3 = 1 1 + 12k + -7k = 1 + k + 2k Combine like terms: 12k + -7k = 5k 1 + 5k = 1 + k + 2k Combine like terms: k + 2k = 3k 1 + 5k = 1 + 3k Add '-1' to each side of the equation. 1 + -1 + 5k = 1 + -1 + 3k Combine like terms: 1 + -1 = 0 0 + 5k = 1 + -1 + 3k 5k = 1 + -1 + 3k Combine like terms: 1 + -1 = 0 5k = 0 + 3k 5k = 3k Solving 5k = 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 5k + -3k = 3k + -3k Combine like terms: 5k + -3k = 2k 2k = 3k + -3k Combine like terms: 3k + -3k = 0 2k = 0 Divide each side by '2'. k = 0 Simplifying k = 0
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