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Simplifying -35 + 8k = 7(1 + 7k) + -1 -35 + 8k = (1 * 7 + 7k * 7) + -1 -35 + 8k = (7 + 49k) + -1 Reorder the terms: -35 + 8k = 7 + -1 + 49k Combine like terms: 7 + -1 = 6 -35 + 8k = 6 + 49k Solving -35 + 8k = 6 + 49k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-49k' to each side of the equation. -35 + 8k + -49k = 6 + 49k + -49k Combine like terms: 8k + -49k = -41k -35 + -41k = 6 + 49k + -49k Combine like terms: 49k + -49k = 0 -35 + -41k = 6 + 0 -35 + -41k = 6 Add '35' to each side of the equation. -35 + 35 + -41k = 6 + 35 Combine like terms: -35 + 35 = 0 0 + -41k = 6 + 35 -41k = 6 + 35 Combine like terms: 6 + 35 = 41 -41k = 41 Divide each side by '-41'. k = -1 Simplifying k = -1
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