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Simplifying -1k + 4(5k + 6) = 3(5 + 7k) + -1 Reorder the terms: -1k + 4(6 + 5k) = 3(5 + 7k) + -1 -1k + (6 * 4 + 5k * 4) = 3(5 + 7k) + -1 -1k + (24 + 20k) = 3(5 + 7k) + -1 Reorder the terms: 24 + -1k + 20k = 3(5 + 7k) + -1 Combine like terms: -1k + 20k = 19k 24 + 19k = 3(5 + 7k) + -1 24 + 19k = (5 * 3 + 7k * 3) + -1 24 + 19k = (15 + 21k) + -1 Reorder the terms: 24 + 19k = 15 + -1 + 21k Combine like terms: 15 + -1 = 14 24 + 19k = 14 + 21k Solving 24 + 19k = 14 + 21k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-21k' to each side of the equation. 24 + 19k + -21k = 14 + 21k + -21k Combine like terms: 19k + -21k = -2k 24 + -2k = 14 + 21k + -21k Combine like terms: 21k + -21k = 0 24 + -2k = 14 + 0 24 + -2k = 14 Add '-24' to each side of the equation. 24 + -24 + -2k = 14 + -24 Combine like terms: 24 + -24 = 0 0 + -2k = 14 + -24 -2k = 14 + -24 Combine like terms: 14 + -24 = -10 -2k = -10 Divide each side by '-2'. k = 5 Simplifying k = 5
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