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Simplifying 8(k + 1) + -1(7k + -5) = 2 Reorder the terms: 8(1 + k) + -1(7k + -5) = 2 (1 * 8 + k * 8) + -1(7k + -5) = 2 (8 + 8k) + -1(7k + -5) = 2 Reorder the terms: 8 + 8k + -1(-5 + 7k) = 2 8 + 8k + (-5 * -1 + 7k * -1) = 2 8 + 8k + (5 + -7k) = 2 Reorder the terms: 8 + 5 + 8k + -7k = 2 Combine like terms: 8 + 5 = 13 13 + 8k + -7k = 2 Combine like terms: 8k + -7k = 1k 13 + 1k = 2 Solving 13 + 1k = 2 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 1k = 2 + -13 Combine like terms: 13 + -13 = 0 0 + 1k = 2 + -13 1k = 2 + -13 Combine like terms: 2 + -13 = -11 1k = -11 Divide each side by '1'. k = -11 Simplifying k = -11
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