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Simplifying 4(3 + 5k) + 7(k + 4) = 8k + 3 + k + 1 (3 * 4 + 5k * 4) + 7(k + 4) = 8k + 3 + k + 1 (12 + 20k) + 7(k + 4) = 8k + 3 + k + 1 Reorder the terms: 12 + 20k + 7(4 + k) = 8k + 3 + k + 1 12 + 20k + (4 * 7 + k * 7) = 8k + 3 + k + 1 12 + 20k + (28 + 7k) = 8k + 3 + k + 1 Reorder the terms: 12 + 28 + 20k + 7k = 8k + 3 + k + 1 Combine like terms: 12 + 28 = 40 40 + 20k + 7k = 8k + 3 + k + 1 Combine like terms: 20k + 7k = 27k 40 + 27k = 8k + 3 + k + 1 Reorder the terms: 40 + 27k = 3 + 1 + 8k + k Combine like terms: 3 + 1 = 4 40 + 27k = 4 + 8k + k Combine like terms: 8k + k = 9k 40 + 27k = 4 + 9k Solving 40 + 27k = 4 + 9k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-9k' to each side of the equation. 40 + 27k + -9k = 4 + 9k + -9k Combine like terms: 27k + -9k = 18k 40 + 18k = 4 + 9k + -9k Combine like terms: 9k + -9k = 0 40 + 18k = 4 + 0 40 + 18k = 4 Add '-40' to each side of the equation. 40 + -40 + 18k = 4 + -40 Combine like terms: 40 + -40 = 0 0 + 18k = 4 + -40 18k = 4 + -40 Combine like terms: 4 + -40 = -36 18k = -36 Divide each side by '18'. k = -2 Simplifying k = -2
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