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Simplifying 5k + 4(0.5k + -6) = k + (12 + -2k) * 2 + 12 Reorder the terms: 5k + 4(-6 + 0.5k) = k + (12 + -2k) * 2 + 12 5k + (-6 * 4 + 0.5k * 4) = k + (12 + -2k) * 2 + 12 5k + (-24 + 2k) = k + (12 + -2k) * 2 + 12 Reorder the terms: -24 + 5k + 2k = k + (12 + -2k) * 2 + 12 Combine like terms: 5k + 2k = 7k -24 + 7k = k + (12 + -2k) * 2 + 12 Reorder the terms for easier multiplication: -24 + 7k = k + 2(12 + -2k) + 12 -24 + 7k = k + (12 * 2 + -2k * 2) + 12 -24 + 7k = k + (24 + -4k) + 12 Reorder the terms: -24 + 7k = 24 + 12 + k + -4k Combine like terms: 24 + 12 = 36 -24 + 7k = 36 + k + -4k Combine like terms: k + -4k = -3k -24 + 7k = 36 + -3k Solving -24 + 7k = 36 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -24 + 7k + 3k = 36 + -3k + 3k Combine like terms: 7k + 3k = 10k -24 + 10k = 36 + -3k + 3k Combine like terms: -3k + 3k = 0 -24 + 10k = 36 + 0 -24 + 10k = 36 Add '24' to each side of the equation. -24 + 24 + 10k = 36 + 24 Combine like terms: -24 + 24 = 0 0 + 10k = 36 + 24 10k = 36 + 24 Combine like terms: 36 + 24 = 60 10k = 60 Divide each side by '10'. k = 6 Simplifying k = 6
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