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Simplifying 6k + 5(1 + k) = 5(1 + 7k) 6k + (1 * 5 + k * 5) = 5(1 + 7k) 6k + (5 + 5k) = 5(1 + 7k) Reorder the terms: 5 + 6k + 5k = 5(1 + 7k) Combine like terms: 6k + 5k = 11k 5 + 11k = 5(1 + 7k) 5 + 11k = (1 * 5 + 7k * 5) 5 + 11k = (5 + 35k) Add '-5' to each side of the equation. 5 + -5 + 11k = 5 + -5 + 35k Combine like terms: 5 + -5 = 0 0 + 11k = 5 + -5 + 35k 11k = 5 + -5 + 35k Combine like terms: 5 + -5 = 0 11k = 0 + 35k 11k = 35k Solving 11k = 35k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-35k' to each side of the equation. 11k + -35k = 35k + -35k Combine like terms: 11k + -35k = -24k -24k = 35k + -35k Combine like terms: 35k + -35k = 0 -24k = 0 Divide each side by '-24'. k = 0 Simplifying k = 0
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