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Simplifying 11(7 + -1k) + 5 = -5(k + -4) + -4 (7 * 11 + -1k * 11) + 5 = -5(k + -4) + -4 (77 + -11k) + 5 = -5(k + -4) + -4 Reorder the terms: 77 + 5 + -11k = -5(k + -4) + -4 Combine like terms: 77 + 5 = 82 82 + -11k = -5(k + -4) + -4 Reorder the terms: 82 + -11k = -5(-4 + k) + -4 82 + -11k = (-4 * -5 + k * -5) + -4 82 + -11k = (20 + -5k) + -4 Reorder the terms: 82 + -11k = 20 + -4 + -5k Combine like terms: 20 + -4 = 16 82 + -11k = 16 + -5k Solving 82 + -11k = 16 + -5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5k' to each side of the equation. 82 + -11k + 5k = 16 + -5k + 5k Combine like terms: -11k + 5k = -6k 82 + -6k = 16 + -5k + 5k Combine like terms: -5k + 5k = 0 82 + -6k = 16 + 0 82 + -6k = 16 Add '-82' to each side of the equation. 82 + -82 + -6k = 16 + -82 Combine like terms: 82 + -82 = 0 0 + -6k = 16 + -82 -6k = 16 + -82 Combine like terms: 16 + -82 = -66 -6k = -66 Divide each side by '-6'. k = 11 Simplifying k = 11
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