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Simplifying k + -5k = 5(-2k + -3) + -1(1 + -7k) Combine like terms: k + -5k = -4k -4k = 5(-2k + -3) + -1(1 + -7k) Reorder the terms: -4k = 5(-3 + -2k) + -1(1 + -7k) -4k = (-3 * 5 + -2k * 5) + -1(1 + -7k) -4k = (-15 + -10k) + -1(1 + -7k) -4k = -15 + -10k + (1 * -1 + -7k * -1) -4k = -15 + -10k + (-1 + 7k) Reorder the terms: -4k = -15 + -1 + -10k + 7k Combine like terms: -15 + -1 = -16 -4k = -16 + -10k + 7k Combine like terms: -10k + 7k = -3k -4k = -16 + -3k Solving -4k = -16 + -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. -4k + 3k = -16 + -3k + 3k Combine like terms: -4k + 3k = -1k -1k = -16 + -3k + 3k Combine like terms: -3k + 3k = 0 -1k = -16 + 0 -1k = -16 Divide each side by '-1'. k = 16 Simplifying k = 16
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