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Simplifying -7.5k + 3.2 + 3.8k + 0.9 = 0.1k + -2.1 + -3.4 + k Reorder the terms: 3.2 + 0.9 + -7.5k + 3.8k = 0.1k + -2.1 + -3.4 + k Combine like terms: 3.2 + 0.9 = 4.1 4.1 + -7.5k + 3.8k = 0.1k + -2.1 + -3.4 + k Combine like terms: -7.5k + 3.8k = -3.7k 4.1 + -3.7k = 0.1k + -2.1 + -3.4 + k Reorder the terms: 4.1 + -3.7k = -2.1 + -3.4 + 0.1k + k Combine like terms: -2.1 + -3.4 = -5.5 4.1 + -3.7k = -5.5 + 0.1k + k Combine like terms: 0.1k + k = 1.1k 4.1 + -3.7k = -5.5 + 1.1k Solving 4.1 + -3.7k = -5.5 + 1.1k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.1k' to each side of the equation. 4.1 + -3.7k + -1.1k = -5.5 + 1.1k + -1.1k Combine like terms: -3.7k + -1.1k = -4.8k 4.1 + -4.8k = -5.5 + 1.1k + -1.1k Combine like terms: 1.1k + -1.1k = 0.0 4.1 + -4.8k = -5.5 + 0.0 4.1 + -4.8k = -5.5 Add '-4.1' to each side of the equation. 4.1 + -4.1 + -4.8k = -5.5 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + -4.8k = -5.5 + -4.1 -4.8k = -5.5 + -4.1 Combine like terms: -5.5 + -4.1 = -9.6 -4.8k = -9.6 Divide each side by '-4.8'. k = 2 Simplifying k = 2
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