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Simplifying 4(k + 3) + 8k = 3k + 75 Reorder the terms: 4(3 + k) + 8k = 3k + 75 (3 * 4 + k * 4) + 8k = 3k + 75 (12 + 4k) + 8k = 3k + 75 Combine like terms: 4k + 8k = 12k 12 + 12k = 3k + 75 Reorder the terms: 12 + 12k = 75 + 3k Solving 12 + 12k = 75 + 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. 12 + 12k + -3k = 75 + 3k + -3k Combine like terms: 12k + -3k = 9k 12 + 9k = 75 + 3k + -3k Combine like terms: 3k + -3k = 0 12 + 9k = 75 + 0 12 + 9k = 75 Add '-12' to each side of the equation. 12 + -12 + 9k = 75 + -12 Combine like terms: 12 + -12 = 0 0 + 9k = 75 + -12 9k = 75 + -12 Combine like terms: 75 + -12 = 63 9k = 63 Divide each side by '9'. k = 7 Simplifying k = 7
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