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Simplifying 6k + 6(1 + -7k) = 39 + -3k 6k + (1 * 6 + -7k * 6) = 39 + -3k 6k + (6 + -42k) = 39 + -3k Reorder the terms: 6 + 6k + -42k = 39 + -3k Combine like terms: 6k + -42k = -36k 6 + -36k = 39 + -3k Solving 6 + -36k = 39 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. 6 + -36k + 3k = 39 + -3k + 3k Combine like terms: -36k + 3k = -33k 6 + -33k = 39 + -3k + 3k Combine like terms: -3k + 3k = 0 6 + -33k = 39 + 0 6 + -33k = 39 Add '-6' to each side of the equation. 6 + -6 + -33k = 39 + -6 Combine like terms: 6 + -6 = 0 0 + -33k = 39 + -6 -33k = 39 + -6 Combine like terms: 39 + -6 = 33 -33k = 33 Divide each side by '-33'. k = -1 Simplifying k = -1
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