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Simplifying 9(1 + 3k) = 11(k + 11) (1 * 9 + 3k * 9) = 11(k + 11) (9 + 27k) = 11(k + 11) Reorder the terms: 9 + 27k = 11(11 + k) 9 + 27k = (11 * 11 + k * 11) 9 + 27k = (121 + 11k) Solving 9 + 27k = 121 + 11k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11k' to each side of the equation. 9 + 27k + -11k = 121 + 11k + -11k Combine like terms: 27k + -11k = 16k 9 + 16k = 121 + 11k + -11k Combine like terms: 11k + -11k = 0 9 + 16k = 121 + 0 9 + 16k = 121 Add '-9' to each side of the equation. 9 + -9 + 16k = 121 + -9 Combine like terms: 9 + -9 = 0 0 + 16k = 121 + -9 16k = 121 + -9 Combine like terms: 121 + -9 = 112 16k = 112 Divide each side by '16'. k = 7 Simplifying k = 7
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