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Simplifying 5(2k + 1) = 3(k + 4) Reorder the terms: 5(1 + 2k) = 3(k + 4) (1 * 5 + 2k * 5) = 3(k + 4) (5 + 10k) = 3(k + 4) Reorder the terms: 5 + 10k = 3(4 + k) 5 + 10k = (4 * 3 + k * 3) 5 + 10k = (12 + 3k) Solving 5 + 10k = 12 + 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 5 + 10k + -3k = 12 + 3k + -3k Combine like terms: 10k + -3k = 7k 5 + 7k = 12 + 3k + -3k Combine like terms: 3k + -3k = 0 5 + 7k = 12 + 0 5 + 7k = 12 Add '-5' to each side of the equation. 5 + -5 + 7k = 12 + -5 Combine like terms: 5 + -5 = 0 0 + 7k = 12 + -5 7k = 12 + -5 Combine like terms: 12 + -5 = 7 7k = 7 Divide each side by '7'. k = 1 Simplifying k = 1
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