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Simplifying k + -7 + 8 = 2(1 + 4k) + -3(-5 + 3k) Reorder the terms: -7 + 8 + k = 2(1 + 4k) + -3(-5 + 3k) Combine like terms: -7 + 8 = 1 1 + k = 2(1 + 4k) + -3(-5 + 3k) 1 + k = (1 * 2 + 4k * 2) + -3(-5 + 3k) 1 + k = (2 + 8k) + -3(-5 + 3k) 1 + k = 2 + 8k + (-5 * -3 + 3k * -3) 1 + k = 2 + 8k + (15 + -9k) Reorder the terms: 1 + k = 2 + 15 + 8k + -9k Combine like terms: 2 + 15 = 17 1 + k = 17 + 8k + -9k Combine like terms: 8k + -9k = -1k 1 + k = 17 + -1k Solving 1 + k = 17 + -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. 1 + k + k = 17 + -1k + k Combine like terms: k + k = 2k 1 + 2k = 17 + -1k + k Combine like terms: -1k + k = 0 1 + 2k = 17 + 0 1 + 2k = 17 Add '-1' to each side of the equation. 1 + -1 + 2k = 17 + -1 Combine like terms: 1 + -1 = 0 0 + 2k = 17 + -1 2k = 17 + -1 Combine like terms: 17 + -1 = 16 2k = 16 Divide each side by '2'. k = 8 Simplifying k = 8
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