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Simplifying -8 = 4(3 + -8k) + -4(8 + -5k) -8 = (3 * 4 + -8k * 4) + -4(8 + -5k) -8 = (12 + -32k) + -4(8 + -5k) -8 = 12 + -32k + (8 * -4 + -5k * -4) -8 = 12 + -32k + (-32 + 20k) Reorder the terms: -8 = 12 + -32 + -32k + 20k Combine like terms: 12 + -32 = -20 -8 = -20 + -32k + 20k Combine like terms: -32k + 20k = -12k -8 = -20 + -12k Solving -8 = -20 + -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. -8 + 12k = -20 + -12k + 12k Combine like terms: -12k + 12k = 0 -8 + 12k = -20 + 0 -8 + 12k = -20 Add '8' to each side of the equation. -8 + 8 + 12k = -20 + 8 Combine like terms: -8 + 8 = 0 0 + 12k = -20 + 8 12k = -20 + 8 Combine like terms: -20 + 8 = -12 12k = -12 Divide each side by '12'. k = -1 Simplifying k = -1
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