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Simplifying 5(20 + k) = 2(30 + k) (20 * 5 + k * 5) = 2(30 + k) (100 + 5k) = 2(30 + k) 100 + 5k = (30 * 2 + k * 2) 100 + 5k = (60 + 2k) Solving 100 + 5k = 60 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 100 + 5k + -2k = 60 + 2k + -2k Combine like terms: 5k + -2k = 3k 100 + 3k = 60 + 2k + -2k Combine like terms: 2k + -2k = 0 100 + 3k = 60 + 0 100 + 3k = 60 Add '-100' to each side of the equation. 100 + -100 + 3k = 60 + -100 Combine like terms: 100 + -100 = 0 0 + 3k = 60 + -100 3k = 60 + -100 Combine like terms: 60 + -100 = -40 3k = -40 Divide each side by '3'. k = -13.33333333 Simplifying k = -13.33333333
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