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Simplifying 2(1 + 6k) = -1 + 3(5k + 1) (1 * 2 + 6k * 2) = -1 + 3(5k + 1) (2 + 12k) = -1 + 3(5k + 1) Reorder the terms: 2 + 12k = -1 + 3(1 + 5k) 2 + 12k = -1 + (1 * 3 + 5k * 3) 2 + 12k = -1 + (3 + 15k) Combine like terms: -1 + 3 = 2 2 + 12k = 2 + 15k Add '-2' to each side of the equation. 2 + -2 + 12k = 2 + -2 + 15k Combine like terms: 2 + -2 = 0 0 + 12k = 2 + -2 + 15k 12k = 2 + -2 + 15k Combine like terms: 2 + -2 = 0 12k = 0 + 15k 12k = 15k Solving 12k = 15k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-15k' to each side of the equation. 12k + -15k = 15k + -15k Combine like terms: 12k + -15k = -3k -3k = 15k + -15k Combine like terms: 15k + -15k = 0 -3k = 0 Divide each side by '-3'. k = 0 Simplifying k = 0
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