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Simplifying 1 + 5k + 1 + 7k = 6(4k + -3) + 2(5 + -1k) Reorder the terms: 1 + 1 + 5k + 7k = 6(4k + -3) + 2(5 + -1k) Combine like terms: 1 + 1 = 2 2 + 5k + 7k = 6(4k + -3) + 2(5 + -1k) Combine like terms: 5k + 7k = 12k 2 + 12k = 6(4k + -3) + 2(5 + -1k) Reorder the terms: 2 + 12k = 6(-3 + 4k) + 2(5 + -1k) 2 + 12k = (-3 * 6 + 4k * 6) + 2(5 + -1k) 2 + 12k = (-18 + 24k) + 2(5 + -1k) 2 + 12k = -18 + 24k + (5 * 2 + -1k * 2) 2 + 12k = -18 + 24k + (10 + -2k) Reorder the terms: 2 + 12k = -18 + 10 + 24k + -2k Combine like terms: -18 + 10 = -8 2 + 12k = -8 + 24k + -2k Combine like terms: 24k + -2k = 22k 2 + 12k = -8 + 22k Solving 2 + 12k = -8 + 22k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-22k' to each side of the equation. 2 + 12k + -22k = -8 + 22k + -22k Combine like terms: 12k + -22k = -10k 2 + -10k = -8 + 22k + -22k Combine like terms: 22k + -22k = 0 2 + -10k = -8 + 0 2 + -10k = -8 Add '-2' to each side of the equation. 2 + -2 + -10k = -8 + -2 Combine like terms: 2 + -2 = 0 0 + -10k = -8 + -2 -10k = -8 + -2 Combine like terms: -8 + -2 = -10 -10k = -10 Divide each side by '-10'. k = 1 Simplifying k = 1
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