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Simplifying 12 + -4k + 7k + 16 + -3k = k + -2 + 16 + 31 + 7k Reorder the terms: 12 + 16 + -4k + 7k + -3k = k + -2 + 16 + 31 + 7k Combine like terms: 12 + 16 = 28 28 + -4k + 7k + -3k = k + -2 + 16 + 31 + 7k Combine like terms: -4k + 7k = 3k 28 + 3k + -3k = k + -2 + 16 + 31 + 7k Combine like terms: 3k + -3k = 0 28 + 0 = k + -2 + 16 + 31 + 7k 28 = k + -2 + 16 + 31 + 7k Reorder the terms: 28 = -2 + 16 + 31 + k + 7k Combine like terms: -2 + 16 = 14 28 = 14 + 31 + k + 7k Combine like terms: 14 + 31 = 45 28 = 45 + k + 7k Combine like terms: k + 7k = 8k 28 = 45 + 8k Solving 28 = 45 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 28 + -8k = 45 + 8k + -8k Combine like terms: 8k + -8k = 0 28 + -8k = 45 + 0 28 + -8k = 45 Add '-28' to each side of the equation. 28 + -28 + -8k = 45 + -28 Combine like terms: 28 + -28 = 0 0 + -8k = 45 + -28 -8k = 45 + -28 Combine like terms: 45 + -28 = 17 -8k = 17 Divide each side by '-8'. k = -2.125 Simplifying k = -2.125
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