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Simplifying 6 + -1(1 + 2k) = -1(k + -1) 6 + (1 * -1 + 2k * -1) = -1(k + -1) 6 + (-1 + -2k) = -1(k + -1) Combine like terms: 6 + -1 = 5 5 + -2k = -1(k + -1) Reorder the terms: 5 + -2k = -1(-1 + k) 5 + -2k = (-1 * -1 + k * -1) 5 + -2k = (1 + -1k) Solving 5 + -2k = 1 + -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. 5 + -2k + k = 1 + -1k + k Combine like terms: -2k + k = -1k 5 + -1k = 1 + -1k + k Combine like terms: -1k + k = 0 5 + -1k = 1 + 0 5 + -1k = 1 Add '-5' to each side of the equation. 5 + -5 + -1k = 1 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 1 + -5 -1k = 1 + -5 Combine like terms: 1 + -5 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4
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