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Simplifying 6(1 + -1k) + -3k = 7k + -2 (1 * 6 + -1k * 6) + -3k = 7k + -2 (6 + -6k) + -3k = 7k + -2 Combine like terms: -6k + -3k = -9k 6 + -9k = 7k + -2 Reorder the terms: 6 + -9k = -2 + 7k Solving 6 + -9k = -2 + 7k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7k' to each side of the equation. 6 + -9k + -7k = -2 + 7k + -7k Combine like terms: -9k + -7k = -16k 6 + -16k = -2 + 7k + -7k Combine like terms: 7k + -7k = 0 6 + -16k = -2 + 0 6 + -16k = -2 Add '-6' to each side of the equation. 6 + -6 + -16k = -2 + -6 Combine like terms: 6 + -6 = 0 0 + -16k = -2 + -6 -16k = -2 + -6 Combine like terms: -2 + -6 = -8 -16k = -8 Divide each side by '-16'. k = 0.5 Simplifying k = 0.5
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