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Simplifying 3k + -2 + k + -5 = -6(4 + -1k) + -1(3 + 7k) Reorder the terms: -2 + -5 + 3k + k = -6(4 + -1k) + -1(3 + 7k) Combine like terms: -2 + -5 = -7 -7 + 3k + k = -6(4 + -1k) + -1(3 + 7k) Combine like terms: 3k + k = 4k -7 + 4k = -6(4 + -1k) + -1(3 + 7k) -7 + 4k = (4 * -6 + -1k * -6) + -1(3 + 7k) -7 + 4k = (-24 + 6k) + -1(3 + 7k) -7 + 4k = -24 + 6k + (3 * -1 + 7k * -1) -7 + 4k = -24 + 6k + (-3 + -7k) Reorder the terms: -7 + 4k = -24 + -3 + 6k + -7k Combine like terms: -24 + -3 = -27 -7 + 4k = -27 + 6k + -7k Combine like terms: 6k + -7k = -1k -7 + 4k = -27 + -1k Solving -7 + 4k = -27 + -1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add 'k' to each side of the equation. -7 + 4k + k = -27 + -1k + k Combine like terms: 4k + k = 5k -7 + 5k = -27 + -1k + k Combine like terms: -1k + k = 0 -7 + 5k = -27 + 0 -7 + 5k = -27 Add '7' to each side of the equation. -7 + 7 + 5k = -27 + 7 Combine like terms: -7 + 7 = 0 0 + 5k = -27 + 7 5k = -27 + 7 Combine like terms: -27 + 7 = -20 5k = -20 Divide each side by '5'. k = -4 Simplifying k = -4
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