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Simplifying -6(1 + -7k) + 7(1 + 6k) = -2 (1 * -6 + -7k * -6) + 7(1 + 6k) = -2 (-6 + 42k) + 7(1 + 6k) = -2 -6 + 42k + (1 * 7 + 6k * 7) = -2 -6 + 42k + (7 + 42k) = -2 Reorder the terms: -6 + 7 + 42k + 42k = -2 Combine like terms: -6 + 7 = 1 1 + 42k + 42k = -2 Combine like terms: 42k + 42k = 84k 1 + 84k = -2 Solving 1 + 84k = -2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 84k = -2 + -1 Combine like terms: 1 + -1 = 0 0 + 84k = -2 + -1 84k = -2 + -1 Combine like terms: -2 + -1 = -3 84k = -3 Divide each side by '84'. k = -0.03571428571 Simplifying k = -0.03571428571
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