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Simplifying 7(k + 3) = 42(12 + -1k) Reorder the terms: 7(3 + k) = 42(12 + -1k) (3 * 7 + k * 7) = 42(12 + -1k) (21 + 7k) = 42(12 + -1k) 21 + 7k = (12 * 42 + -1k * 42) 21 + 7k = (504 + -42k) Solving 21 + 7k = 504 + -42k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '42k' to each side of the equation. 21 + 7k + 42k = 504 + -42k + 42k Combine like terms: 7k + 42k = 49k 21 + 49k = 504 + -42k + 42k Combine like terms: -42k + 42k = 0 21 + 49k = 504 + 0 21 + 49k = 504 Add '-21' to each side of the equation. 21 + -21 + 49k = 504 + -21 Combine like terms: 21 + -21 = 0 0 + 49k = 504 + -21 49k = 504 + -21 Combine like terms: 504 + -21 = 483 49k = 483 Divide each side by '49'. k = 9.857142857 Simplifying k = 9.857142857
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