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Simplifying 6k + -35 = 2 + 7(7k + 7) Reorder the terms: -35 + 6k = 2 + 7(7k + 7) Reorder the terms: -35 + 6k = 2 + 7(7 + 7k) -35 + 6k = 2 + (7 * 7 + 7k * 7) -35 + 6k = 2 + (49 + 49k) Combine like terms: 2 + 49 = 51 -35 + 6k = 51 + 49k Solving -35 + 6k = 51 + 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 + 6k + -49k = 51 + 49k + -49k Combine like terms: 6k + -49k = -43k -35 + -43k = 51 + 49k + -49k Combine like terms: 49k + -49k = 0 -35 + -43k = 51 + 0 -35 + -43k = 51 Add '35' to each side of the equation. -35 + 35 + -43k = 51 + 35 Combine like terms: -35 + 35 = 0 0 + -43k = 51 + 35 -43k = 51 + 35 Combine like terms: 51 + 35 = 86 -43k = 86 Divide each side by '-43'. k = -2 Simplifying k = -2
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