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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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