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Simplifying K + 5 + 8k = 2(1 + 7k) + -3(k + 5) Reorder the terms: 5 + K + 8k = 2(1 + 7k) + -3(k + 5) 5 + K + 8k = (1 * 2 + 7k * 2) + -3(k + 5) 5 + K + 8k = (2 + 14k) + -3(k + 5) Reorder the terms: 5 + K + 8k = 2 + 14k + -3(5 + k) 5 + K + 8k = 2 + 14k + (5 * -3 + k * -3) 5 + K + 8k = 2 + 14k + (-15 + -3k) Reorder the terms: 5 + K + 8k = 2 + -15 + 14k + -3k Combine like terms: 2 + -15 = -13 5 + K + 8k = -13 + 14k + -3k Combine like terms: 14k + -3k = 11k 5 + K + 8k = -13 + 11k Solving 5 + K + 8k = -13 + 11k Solving for variable 'K'. Move all terms containing K to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + K + -5 + 8k = -13 + -5 + 11k Reorder the terms: 5 + -5 + K + 8k = -13 + -5 + 11k Combine like terms: 5 + -5 = 0 0 + K + 8k = -13 + -5 + 11k K + 8k = -13 + -5 + 11k Combine like terms: -13 + -5 = -18 K + 8k = -18 + 11k Add '-8k' to each side of the equation. K + 8k + -8k = -18 + 11k + -8k Combine like terms: 8k + -8k = 0 K + 0 = -18 + 11k + -8k K = -18 + 11k + -8k Combine like terms: 11k + -8k = 3k K = -18 + 3k Simplifying K = -18 + 3k
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