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Simplifying -1(1 + 5k) + 8k = -7(-7 + k) (1 * -1 + 5k * -1) + 8k = -7(-7 + k) (-1 + -5k) + 8k = -7(-7 + k) Combine like terms: -5k + 8k = 3k -1 + 3k = -7(-7 + k) -1 + 3k = (-7 * -7 + k * -7) -1 + 3k = (49 + -7k) Solving -1 + 3k = 49 + -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. -1 + 3k + 7k = 49 + -7k + 7k Combine like terms: 3k + 7k = 10k -1 + 10k = 49 + -7k + 7k Combine like terms: -7k + 7k = 0 -1 + 10k = 49 + 0 -1 + 10k = 49 Add '1' to each side of the equation. -1 + 1 + 10k = 49 + 1 Combine like terms: -1 + 1 = 0 0 + 10k = 49 + 1 10k = 49 + 1 Combine like terms: 49 + 1 = 50 10k = 50 Divide each side by '10'. k = 5 Simplifying k = 5
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