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Simplifying 5(0.2k + -0.1) + 7k = 1.9 Reorder the terms: 5(-0.1 + 0.2k) + 7k = 1.9 (-0.1 * 5 + 0.2k * 5) + 7k = 1.9 (-0.5 + 1k) + 7k = 1.9 Combine like terms: 1k + 7k = 8k -0.5 + 8k = 1.9 Solving -0.5 + 8k = 1.9 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + 8k = 1.9 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 8k = 1.9 + 0.5 8k = 1.9 + 0.5 Combine like terms: 1.9 + 0.5 = 2.4 8k = 2.4 Divide each side by '8'. k = 0.3 Simplifying k = 0.3
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