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Simplifying -83 = 4(1 + -3k) + -3 -83 = (1 * 4 + -3k * 4) + -3 -83 = (4 + -12k) + -3 Reorder the terms: -83 = 4 + -3 + -12k Combine like terms: 4 + -3 = 1 -83 = 1 + -12k Solving -83 = 1 + -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. -83 + 12k = 1 + -12k + 12k Combine like terms: -12k + 12k = 0 -83 + 12k = 1 + 0 -83 + 12k = 1 Add '83' to each side of the equation. -83 + 83 + 12k = 1 + 83 Combine like terms: -83 + 83 = 0 0 + 12k = 1 + 83 12k = 1 + 83 Combine like terms: 1 + 83 = 84 12k = 84 Divide each side by '12'. k = 7 Simplifying k = 7
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