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Simplifying -3(2.5 + -1k) + 0.5(7 + 8k) = 0 (2.5 * -3 + -1k * -3) + 0.5(7 + 8k) = 0 (-7.5 + 3k) + 0.5(7 + 8k) = 0 -7.5 + 3k + (7 * 0.5 + 8k * 0.5) = 0 -7.5 + 3k + (3.5 + 4k) = 0 Reorder the terms: -7.5 + 3.5 + 3k + 4k = 0 Combine like terms: -7.5 + 3.5 = -4 -4 + 3k + 4k = 0 Combine like terms: 3k + 4k = 7k -4 + 7k = 0 Solving -4 + 7k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 7k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7k = 0 + 4 7k = 0 + 4 Combine like terms: 0 + 4 = 4 7k = 4 Divide each side by '7'. k = 0.5714285714 Simplifying k = 0.5714285714
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