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Simplifying 27 = -5(-7 + 3k) + -8(-6 + -1k) 27 = (-7 * -5 + 3k * -5) + -8(-6 + -1k) 27 = (35 + -15k) + -8(-6 + -1k) 27 = 35 + -15k + (-6 * -8 + -1k * -8) 27 = 35 + -15k + (48 + 8k) Reorder the terms: 27 = 35 + 48 + -15k + 8k Combine like terms: 35 + 48 = 83 27 = 83 + -15k + 8k Combine like terms: -15k + 8k = -7k 27 = 83 + -7k Solving 27 = 83 + -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. 27 + 7k = 83 + -7k + 7k Combine like terms: -7k + 7k = 0 27 + 7k = 83 + 0 27 + 7k = 83 Add '-27' to each side of the equation. 27 + -27 + 7k = 83 + -27 Combine like terms: 27 + -27 = 0 0 + 7k = 83 + -27 7k = 83 + -27 Combine like terms: 83 + -27 = 56 7k = 56 Divide each side by '7'. k = 8 Simplifying k = 8
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