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Simplifying -6(2 + -1k) + 3k + -1(4 + 7k) = 2 (2 * -6 + -1k * -6) + 3k + -1(4 + 7k) = 2 (-12 + 6k) + 3k + -1(4 + 7k) = 2 -12 + 6k + 3k + (4 * -1 + 7k * -1) = 2 -12 + 6k + 3k + (-4 + -7k) = 2 Reorder the terms: -12 + -4 + 6k + 3k + -7k = 2 Combine like terms: -12 + -4 = -16 -16 + 6k + 3k + -7k = 2 Combine like terms: 6k + 3k = 9k -16 + 9k + -7k = 2 Combine like terms: 9k + -7k = 2k -16 + 2k = 2 Solving -16 + 2k = 2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + 2k = 2 + 16 Combine like terms: -16 + 16 = 0 0 + 2k = 2 + 16 2k = 2 + 16 Combine like terms: 2 + 16 = 18 2k = 18 Divide each side by '2'. k = 9 Simplifying k = 9
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