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Simplifying 7(4 + 3k) + 7(7 + -1k) = 2k + 5k (4 * 7 + 3k * 7) + 7(7 + -1k) = 2k + 5k (28 + 21k) + 7(7 + -1k) = 2k + 5k 28 + 21k + (7 * 7 + -1k * 7) = 2k + 5k 28 + 21k + (49 + -7k) = 2k + 5k Reorder the terms: 28 + 49 + 21k + -7k = 2k + 5k Combine like terms: 28 + 49 = 77 77 + 21k + -7k = 2k + 5k Combine like terms: 21k + -7k = 14k 77 + 14k = 2k + 5k Combine like terms: 2k + 5k = 7k 77 + 14k = 7k Solving 77 + 14k = 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. 77 + 14k + -7k = 7k + -7k Combine like terms: 14k + -7k = 7k 77 + 7k = 7k + -7k Combine like terms: 7k + -7k = 0 77 + 7k = 0 Add '-77' to each side of the equation. 77 + -77 + 7k = 0 + -77 Combine like terms: 77 + -77 = 0 0 + 7k = 0 + -77 7k = 0 + -77 Combine like terms: 0 + -77 = -77 7k = -77 Divide each side by '7'. k = -11 Simplifying k = -11
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