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Simplifying 8[12 + -1k] = 3[k + 21] [12 * 8 + -1k * 8] = 3[k + 21] [96 + -8k] = 3[k + 21] Reorder the terms: 96 + -8k = 3[21 + k] 96 + -8k = [21 * 3 + k * 3] 96 + -8k = [63 + 3k] Solving 96 + -8k = 63 + 3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3k' to each side of the equation. 96 + -8k + -3k = 63 + 3k + -3k Combine like terms: -8k + -3k = -11k 96 + -11k = 63 + 3k + -3k Combine like terms: 3k + -3k = 0 96 + -11k = 63 + 0 96 + -11k = 63 Add '-96' to each side of the equation. 96 + -96 + -11k = 63 + -96 Combine like terms: 96 + -96 = 0 0 + -11k = 63 + -96 -11k = 63 + -96 Combine like terms: 63 + -96 = -33 -11k = -33 Divide each side by '-11'. k = 3 Simplifying k = 3
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