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Simplifying -1(5k + 1) = 2(1 + -7k) + k Reorder the terms: -1(1 + 5k) = 2(1 + -7k) + k (1 * -1 + 5k * -1) = 2(1 + -7k) + k (-1 + -5k) = 2(1 + -7k) + k -1 + -5k = (1 * 2 + -7k * 2) + k -1 + -5k = (2 + -14k) + k Combine like terms: -14k + k = -13k -1 + -5k = 2 + -13k Solving -1 + -5k = 2 + -13k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '13k' to each side of the equation. -1 + -5k + 13k = 2 + -13k + 13k Combine like terms: -5k + 13k = 8k -1 + 8k = 2 + -13k + 13k Combine like terms: -13k + 13k = 0 -1 + 8k = 2 + 0 -1 + 8k = 2 Add '1' to each side of the equation. -1 + 1 + 8k = 2 + 1 Combine like terms: -1 + 1 = 0 0 + 8k = 2 + 1 8k = 2 + 1 Combine like terms: 2 + 1 = 3 8k = 3 Divide each side by '8'. k = 0.375 Simplifying k = 0.375
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