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Simplifying 3(2k + 1) = 5(k + 2) Reorder the terms: 3(1 + 2k) = 5(k + 2) (1 * 3 + 2k * 3) = 5(k + 2) (3 + 6k) = 5(k + 2) Reorder the terms: 3 + 6k = 5(2 + k) 3 + 6k = (2 * 5 + k * 5) 3 + 6k = (10 + 5k) Solving 3 + 6k = 10 + 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. 3 + 6k + -5k = 10 + 5k + -5k Combine like terms: 6k + -5k = 1k 3 + 1k = 10 + 5k + -5k Combine like terms: 5k + -5k = 0 3 + 1k = 10 + 0 3 + 1k = 10 Add '-3' to each side of the equation. 3 + -3 + 1k = 10 + -3 Combine like terms: 3 + -3 = 0 0 + 1k = 10 + -3 1k = 10 + -3 Combine like terms: 10 + -3 = 7 1k = 7 Divide each side by '1'. k = 7 Simplifying k = 7
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