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Simplifying 7(1 + k) + 6(k + 3) = 76 (1 * 7 + k * 7) + 6(k + 3) = 76 (7 + 7k) + 6(k + 3) = 76 Reorder the terms: 7 + 7k + 6(3 + k) = 76 7 + 7k + (3 * 6 + k * 6) = 76 7 + 7k + (18 + 6k) = 76 Reorder the terms: 7 + 18 + 7k + 6k = 76 Combine like terms: 7 + 18 = 25 25 + 7k + 6k = 76 Combine like terms: 7k + 6k = 13k 25 + 13k = 76 Solving 25 + 13k = 76 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 13k = 76 + -25 Combine like terms: 25 + -25 = 0 0 + 13k = 76 + -25 13k = 76 + -25 Combine like terms: 76 + -25 = 51 13k = 51 Divide each side by '13'. k = 3.923076923 Simplifying k = 3.923076923
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