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Simplifying 11 + 11k + -12k + 10 = 4(6 + 2k) + -5(9 + 6k) Reorder the terms: 11 + 10 + 11k + -12k = 4(6 + 2k) + -5(9 + 6k) Combine like terms: 11 + 10 = 21 21 + 11k + -12k = 4(6 + 2k) + -5(9 + 6k) Combine like terms: 11k + -12k = -1k 21 + -1k = 4(6 + 2k) + -5(9 + 6k) 21 + -1k = (6 * 4 + 2k * 4) + -5(9 + 6k) 21 + -1k = (24 + 8k) + -5(9 + 6k) 21 + -1k = 24 + 8k + (9 * -5 + 6k * -5) 21 + -1k = 24 + 8k + (-45 + -30k) Reorder the terms: 21 + -1k = 24 + -45 + 8k + -30k Combine like terms: 24 + -45 = -21 21 + -1k = -21 + 8k + -30k Combine like terms: 8k + -30k = -22k 21 + -1k = -21 + -22k Solving 21 + -1k = -21 + -22k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '22k' to each side of the equation. 21 + -1k + 22k = -21 + -22k + 22k Combine like terms: -1k + 22k = 21k 21 + 21k = -21 + -22k + 22k Combine like terms: -22k + 22k = 0 21 + 21k = -21 + 0 21 + 21k = -21 Add '-21' to each side of the equation. 21 + -21 + 21k = -21 + -21 Combine like terms: 21 + -21 = 0 0 + 21k = -21 + -21 21k = -21 + -21 Combine like terms: -21 + -21 = -42 21k = -42 Divide each side by '21'. k = -2 Simplifying k = -2
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