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Simplifying -2(1 + -2k) + 3k = -6(k + -4) (1 * -2 + -2k * -2) + 3k = -6(k + -4) (-2 + 4k) + 3k = -6(k + -4) Combine like terms: 4k + 3k = 7k -2 + 7k = -6(k + -4) Reorder the terms: -2 + 7k = -6(-4 + k) -2 + 7k = (-4 * -6 + k * -6) -2 + 7k = (24 + -6k) Solving -2 + 7k = 24 + -6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6k' to each side of the equation. -2 + 7k + 6k = 24 + -6k + 6k Combine like terms: 7k + 6k = 13k -2 + 13k = 24 + -6k + 6k Combine like terms: -6k + 6k = 0 -2 + 13k = 24 + 0 -2 + 13k = 24 Add '2' to each side of the equation. -2 + 2 + 13k = 24 + 2 Combine like terms: -2 + 2 = 0 0 + 13k = 24 + 2 13k = 24 + 2 Combine like terms: 24 + 2 = 26 13k = 26 Divide each side by '13'. k = 2 Simplifying k = 2
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