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Simplifying -4(3k + -1) = 4k + -1(8 + -2k) + 12 Reorder the terms: -4(-1 + 3k) = 4k + -1(8 + -2k) + 12 (-1 * -4 + 3k * -4) = 4k + -1(8 + -2k) + 12 (4 + -12k) = 4k + -1(8 + -2k) + 12 4 + -12k = 4k + (8 * -1 + -2k * -1) + 12 4 + -12k = 4k + (-8 + 2k) + 12 Reorder the terms: 4 + -12k = -8 + 12 + 4k + 2k Combine like terms: -8 + 12 = 4 4 + -12k = 4 + 4k + 2k Combine like terms: 4k + 2k = 6k 4 + -12k = 4 + 6k Add '-4' to each side of the equation. 4 + -4 + -12k = 4 + -4 + 6k Combine like terms: 4 + -4 = 0 0 + -12k = 4 + -4 + 6k -12k = 4 + -4 + 6k Combine like terms: 4 + -4 = 0 -12k = 0 + 6k -12k = 6k Solving -12k = 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. -12k + -6k = 6k + -6k Combine like terms: -12k + -6k = -18k -18k = 6k + -6k Combine like terms: 6k + -6k = 0 -18k = 0 Divide each side by '-18'. k = 0 Simplifying k = 0
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