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Simplifying 4k + 12(1 + -1k) = -1k + 5(-12 + k) 4k + (1 * 12 + -1k * 12) = -1k + 5(-12 + k) 4k + (12 + -12k) = -1k + 5(-12 + k) Reorder the terms: 12 + 4k + -12k = -1k + 5(-12 + k) Combine like terms: 4k + -12k = -8k 12 + -8k = -1k + 5(-12 + k) 12 + -8k = -1k + (-12 * 5 + k * 5) 12 + -8k = -1k + (-60 + 5k) Reorder the terms: 12 + -8k = -60 + -1k + 5k Combine like terms: -1k + 5k = 4k 12 + -8k = -60 + 4k Solving 12 + -8k = -60 + 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. 12 + -8k + -4k = -60 + 4k + -4k Combine like terms: -8k + -4k = -12k 12 + -12k = -60 + 4k + -4k Combine like terms: 4k + -4k = 0 12 + -12k = -60 + 0 12 + -12k = -60 Add '-12' to each side of the equation. 12 + -12 + -12k = -60 + -12 Combine like terms: 12 + -12 = 0 0 + -12k = -60 + -12 -12k = -60 + -12 Combine like terms: -60 + -12 = -72 -12k = -72 Divide each side by '-12'. k = 6 Simplifying k = 6
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