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Simplifying 0.5(5 + -2k) = 6(k + 4) (5 * 0.5 + -2k * 0.5) = 6(k + 4) (2.5 + -1k) = 6(k + 4) Reorder the terms: 2.5 + -1k = 6(4 + k) 2.5 + -1k = (4 * 6 + k * 6) 2.5 + -1k = (24 + 6k) Solving 2.5 + -1k = 24 + 6k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. 2.5 + -1k + -6k = 24 + 6k + -6k Combine like terms: -1k + -6k = -7k 2.5 + -7k = 24 + 6k + -6k Combine like terms: 6k + -6k = 0 2.5 + -7k = 24 + 0 2.5 + -7k = 24 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -7k = 24 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -7k = 24 + -2.5 -7k = 24 + -2.5 Combine like terms: 24 + -2.5 = 21.5 -7k = 21.5 Divide each side by '-7'. k = -3.071428571 Simplifying k = -3.071428571
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