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Simplifying 9 = 5(-1 + -2k) + -1(6 + -6k) 9 = (-1 * 5 + -2k * 5) + -1(6 + -6k) 9 = (-5 + -10k) + -1(6 + -6k) 9 = -5 + -10k + (6 * -1 + -6k * -1) 9 = -5 + -10k + (-6 + 6k) Reorder the terms: 9 = -5 + -6 + -10k + 6k Combine like terms: -5 + -6 = -11 9 = -11 + -10k + 6k Combine like terms: -10k + 6k = -4k 9 = -11 + -4k Solving 9 = -11 + -4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. 9 + 4k = -11 + -4k + 4k Combine like terms: -4k + 4k = 0 9 + 4k = -11 + 0 9 + 4k = -11 Add '-9' to each side of the equation. 9 + -9 + 4k = -11 + -9 Combine like terms: 9 + -9 = 0 0 + 4k = -11 + -9 4k = -11 + -9 Combine like terms: -11 + -9 = -20 4k = -20 Divide each side by '4'. k = -5 Simplifying k = -5
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