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Simplifying 10 + 10k + -12 = 3(7k + 9) + -9(k + -1) Reorder the terms: 10 + -12 + 10k = 3(7k + 9) + -9(k + -1) Combine like terms: 10 + -12 = -2 -2 + 10k = 3(7k + 9) + -9(k + -1) Reorder the terms: -2 + 10k = 3(9 + 7k) + -9(k + -1) -2 + 10k = (9 * 3 + 7k * 3) + -9(k + -1) -2 + 10k = (27 + 21k) + -9(k + -1) Reorder the terms: -2 + 10k = 27 + 21k + -9(-1 + k) -2 + 10k = 27 + 21k + (-1 * -9 + k * -9) -2 + 10k = 27 + 21k + (9 + -9k) Reorder the terms: -2 + 10k = 27 + 9 + 21k + -9k Combine like terms: 27 + 9 = 36 -2 + 10k = 36 + 21k + -9k Combine like terms: 21k + -9k = 12k -2 + 10k = 36 + 12k Solving -2 + 10k = 36 + 12k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12k' to each side of the equation. -2 + 10k + -12k = 36 + 12k + -12k Combine like terms: 10k + -12k = -2k -2 + -2k = 36 + 12k + -12k Combine like terms: 12k + -12k = 0 -2 + -2k = 36 + 0 -2 + -2k = 36 Add '2' to each side of the equation. -2 + 2 + -2k = 36 + 2 Combine like terms: -2 + 2 = 0 0 + -2k = 36 + 2 -2k = 36 + 2 Combine like terms: 36 + 2 = 38 -2k = 38 Divide each side by '-2'. k = -19 Simplifying k = -19
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