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Simplifying -1(-1k + 1) = -5(1 + -6k) + 7k Reorder the terms: -1(1 + -1k) = -5(1 + -6k) + 7k (1 * -1 + -1k * -1) = -5(1 + -6k) + 7k (-1 + 1k) = -5(1 + -6k) + 7k -1 + 1k = (1 * -5 + -6k * -5) + 7k -1 + 1k = (-5 + 30k) + 7k Combine like terms: 30k + 7k = 37k -1 + 1k = -5 + 37k Solving -1 + 1k = -5 + 37k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-37k' to each side of the equation. -1 + 1k + -37k = -5 + 37k + -37k Combine like terms: 1k + -37k = -36k -1 + -36k = -5 + 37k + -37k Combine like terms: 37k + -37k = 0 -1 + -36k = -5 + 0 -1 + -36k = -5 Add '1' to each side of the equation. -1 + 1 + -36k = -5 + 1 Combine like terms: -1 + 1 = 0 0 + -36k = -5 + 1 -36k = -5 + 1 Combine like terms: -5 + 1 = -4 -36k = -4 Divide each side by '-36'. k = 0.1111111111 Simplifying k = 0.1111111111
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