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Simplifying 7k + -1(5 + 5k) = -2 + -1(1 + -3k) 7k + (5 * -1 + 5k * -1) = -2 + -1(1 + -3k) 7k + (-5 + -5k) = -2 + -1(1 + -3k) Reorder the terms: -5 + 7k + -5k = -2 + -1(1 + -3k) Combine like terms: 7k + -5k = 2k -5 + 2k = -2 + -1(1 + -3k) -5 + 2k = -2 + (1 * -1 + -3k * -1) -5 + 2k = -2 + (-1 + 3k) Combine like terms: -2 + -1 = -3 -5 + 2k = -3 + 3k Solving -5 + 2k = -3 + 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. -5 + 2k + -3k = -3 + 3k + -3k Combine like terms: 2k + -3k = -1k -5 + -1k = -3 + 3k + -3k Combine like terms: 3k + -3k = 0 -5 + -1k = -3 + 0 -5 + -1k = -3 Add '5' to each side of the equation. -5 + 5 + -1k = -3 + 5 Combine like terms: -5 + 5 = 0 0 + -1k = -3 + 5 -1k = -3 + 5 Combine like terms: -3 + 5 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2
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