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Simplifying 5(k + -2k + 1) = 2k + 3(2 + k) Reorder the terms: 5(1 + k + -2k) = 2k + 3(2 + k) Combine like terms: k + -2k = -1k 5(1 + -1k) = 2k + 3(2 + k) (1 * 5 + -1k * 5) = 2k + 3(2 + k) (5 + -5k) = 2k + 3(2 + k) 5 + -5k = 2k + (2 * 3 + k * 3) 5 + -5k = 2k + (6 + 3k) Reorder the terms: 5 + -5k = 6 + 2k + 3k Combine like terms: 2k + 3k = 5k 5 + -5k = 6 + 5k Solving 5 + -5k = 6 + 5k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5k' to each side of the equation. 5 + -5k + -5k = 6 + 5k + -5k Combine like terms: -5k + -5k = -10k 5 + -10k = 6 + 5k + -5k Combine like terms: 5k + -5k = 0 5 + -10k = 6 + 0 5 + -10k = 6 Add '-5' to each side of the equation. 5 + -5 + -10k = 6 + -5 Combine like terms: 5 + -5 = 0 0 + -10k = 6 + -5 -10k = 6 + -5 Combine like terms: 6 + -5 = 1 -10k = 1 Divide each side by '-10'. k = -0.1 Simplifying k = -0.1
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