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Simplifying -6(1 + 7k) = -7(1 + -6k) + -11 (1 * -6 + 7k * -6) = -7(1 + -6k) + -11 (-6 + -42k) = -7(1 + -6k) + -11 -6 + -42k = (1 * -7 + -6k * -7) + -11 -6 + -42k = (-7 + 42k) + -11 Reorder the terms: -6 + -42k = -7 + -11 + 42k Combine like terms: -7 + -11 = -18 -6 + -42k = -18 + 42k Solving -6 + -42k = -18 + 42k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-42k' to each side of the equation. -6 + -42k + -42k = -18 + 42k + -42k Combine like terms: -42k + -42k = -84k -6 + -84k = -18 + 42k + -42k Combine like terms: 42k + -42k = 0 -6 + -84k = -18 + 0 -6 + -84k = -18 Add '6' to each side of the equation. -6 + 6 + -84k = -18 + 6 Combine like terms: -6 + 6 = 0 0 + -84k = -18 + 6 -84k = -18 + 6 Combine like terms: -18 + 6 = -12 -84k = -12 Divide each side by '-84'. k = 0.1428571429 Simplifying k = 0.1428571429
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