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Simplifying 4(3 + -8k) = 6(2 + 2k) + 4 (3 * 4 + -8k * 4) = 6(2 + 2k) + 4 (12 + -32k) = 6(2 + 2k) + 4 12 + -32k = (2 * 6 + 2k * 6) + 4 12 + -32k = (12 + 12k) + 4 Reorder the terms: 12 + -32k = 12 + 4 + 12k Combine like terms: 12 + 4 = 16 12 + -32k = 16 + 12k Solving 12 + -32k = 16 + 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. 12 + -32k + -12k = 16 + 12k + -12k Combine like terms: -32k + -12k = -44k 12 + -44k = 16 + 12k + -12k Combine like terms: 12k + -12k = 0 12 + -44k = 16 + 0 12 + -44k = 16 Add '-12' to each side of the equation. 12 + -12 + -44k = 16 + -12 Combine like terms: 12 + -12 = 0 0 + -44k = 16 + -12 -44k = 16 + -12 Combine like terms: 16 + -12 = 4 -44k = 4 Divide each side by '-44'. k = -0.09090909091 Simplifying k = -0.09090909091
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