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Simplifying 3(4 + 7k) + 6k = -6(1 + -4k) + -6 (4 * 3 + 7k * 3) + 6k = -6(1 + -4k) + -6 (12 + 21k) + 6k = -6(1 + -4k) + -6 Combine like terms: 21k + 6k = 27k 12 + 27k = -6(1 + -4k) + -6 12 + 27k = (1 * -6 + -4k * -6) + -6 12 + 27k = (-6 + 24k) + -6 Reorder the terms: 12 + 27k = -6 + -6 + 24k Combine like terms: -6 + -6 = -12 12 + 27k = -12 + 24k Solving 12 + 27k = -12 + 24k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-24k' to each side of the equation. 12 + 27k + -24k = -12 + 24k + -24k Combine like terms: 27k + -24k = 3k 12 + 3k = -12 + 24k + -24k Combine like terms: 24k + -24k = 0 12 + 3k = -12 + 0 12 + 3k = -12 Add '-12' to each side of the equation. 12 + -12 + 3k = -12 + -12 Combine like terms: 12 + -12 = 0 0 + 3k = -12 + -12 3k = -12 + -12 Combine like terms: -12 + -12 = -24 3k = -24 Divide each side by '3'. k = -8 Simplifying k = -8
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