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Simplifying 0.125(16k + -24) + 0.2(2 + 10k) = 0 Reorder the terms: 0.125(-24 + 16k) + 0.2(2 + 10k) = 0 (-24 * 0.125 + 16k * 0.125) + 0.2(2 + 10k) = 0 (-3 + 2k) + 0.2(2 + 10k) = 0 -3 + 2k + (2 * 0.2 + 10k * 0.2) = 0 -3 + 2k + (0.4 + 2k) = 0 Reorder the terms: -3 + 0.4 + 2k + 2k = 0 Combine like terms: -3 + 0.4 = -2.6 -2.6 + 2k + 2k = 0 Combine like terms: 2k + 2k = 4k -2.6 + 4k = 0 Solving -2.6 + 4k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + 4k = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 4k = 0 + 2.6 4k = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 4k = 2.6 Divide each side by '4'. k = 0.65 Simplifying k = 0.65
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