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Simplifying 3(2k + 1) = 2(4 + -3k) Reorder the terms: 3(1 + 2k) = 2(4 + -3k) (1 * 3 + 2k * 3) = 2(4 + -3k) (3 + 6k) = 2(4 + -3k) 3 + 6k = (4 * 2 + -3k * 2) 3 + 6k = (8 + -6k) Solving 3 + 6k = 8 + -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. 3 + 6k + 6k = 8 + -6k + 6k Combine like terms: 6k + 6k = 12k 3 + 12k = 8 + -6k + 6k Combine like terms: -6k + 6k = 0 3 + 12k = 8 + 0 3 + 12k = 8 Add '-3' to each side of the equation. 3 + -3 + 12k = 8 + -3 Combine like terms: 3 + -3 = 0 0 + 12k = 8 + -3 12k = 8 + -3 Combine like terms: 8 + -3 = 5 12k = 5 Divide each side by '12'. k = 0.4166666667 Simplifying k = 0.4166666667
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