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Simplifying 7k + 1 = 8k + 1 + 6 + -1 Reorder the terms: 1 + 7k = 8k + 1 + 6 + -1 Reorder the terms: 1 + 7k = 1 + 6 + -1 + 8k Combine like terms: 1 + 6 = 7 1 + 7k = 7 + -1 + 8k Combine like terms: 7 + -1 = 6 1 + 7k = 6 + 8k Solving 1 + 7k = 6 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 1 + 7k + -8k = 6 + 8k + -8k Combine like terms: 7k + -8k = -1k 1 + -1k = 6 + 8k + -8k Combine like terms: 8k + -8k = 0 1 + -1k = 6 + 0 1 + -1k = 6 Add '-1' to each side of the equation. 1 + -1 + -1k = 6 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 6 + -1 -1k = 6 + -1 Combine like terms: 6 + -1 = 5 -1k = 5 Divide each side by '-1'. k = -5 Simplifying k = -5
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