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Simplifying 5(k + 3) + 9 = 3(k + -2) + 6 Reorder the terms: 5(3 + k) + 9 = 3(k + -2) + 6 (3 * 5 + k * 5) + 9 = 3(k + -2) + 6 (15 + 5k) + 9 = 3(k + -2) + 6 Reorder the terms: 15 + 9 + 5k = 3(k + -2) + 6 Combine like terms: 15 + 9 = 24 24 + 5k = 3(k + -2) + 6 Reorder the terms: 24 + 5k = 3(-2 + k) + 6 24 + 5k = (-2 * 3 + k * 3) + 6 24 + 5k = (-6 + 3k) + 6 Reorder the terms: 24 + 5k = -6 + 6 + 3k Combine like terms: -6 + 6 = 0 24 + 5k = 0 + 3k 24 + 5k = 3k Solving 24 + 5k = 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 24 + 5k + -3k = 3k + -3k Combine like terms: 5k + -3k = 2k 24 + 2k = 3k + -3k Combine like terms: 3k + -3k = 0 24 + 2k = 0 Add '-24' to each side of the equation. 24 + -24 + 2k = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 2k = 0 + -24 2k = 0 + -24 Combine like terms: 0 + -24 = -24 2k = -24 Divide each side by '2'. k = -12 Simplifying k = -12
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