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Simplifying 7k + 5k = 3(-5k + -4) + 12(1 + k) Combine like terms: 7k + 5k = 12k 12k = 3(-5k + -4) + 12(1 + k) Reorder the terms: 12k = 3(-4 + -5k) + 12(1 + k) 12k = (-4 * 3 + -5k * 3) + 12(1 + k) 12k = (-12 + -15k) + 12(1 + k) 12k = -12 + -15k + (1 * 12 + k * 12) 12k = -12 + -15k + (12 + 12k) Reorder the terms: 12k = -12 + 12 + -15k + 12k Combine like terms: -12 + 12 = 0 12k = 0 + -15k + 12k 12k = -15k + 12k Combine like terms: -15k + 12k = -3k 12k = -3k Solving 12k = -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. 12k + 3k = -3k + 3k Combine like terms: 12k + 3k = 15k 15k = -3k + 3k Combine like terms: -3k + 3k = 0 15k = 0 Divide each side by '15'. k = 0 Simplifying k = 0
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