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Simplifying 9(4k + 1) = 8(k + -1) + 11k Reorder the terms: 9(1 + 4k) = 8(k + -1) + 11k (1 * 9 + 4k * 9) = 8(k + -1) + 11k (9 + 36k) = 8(k + -1) + 11k Reorder the terms: 9 + 36k = 8(-1 + k) + 11k 9 + 36k = (-1 * 8 + k * 8) + 11k 9 + 36k = (-8 + 8k) + 11k Combine like terms: 8k + 11k = 19k 9 + 36k = -8 + 19k Solving 9 + 36k = -8 + 19k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-19k' to each side of the equation. 9 + 36k + -19k = -8 + 19k + -19k Combine like terms: 36k + -19k = 17k 9 + 17k = -8 + 19k + -19k Combine like terms: 19k + -19k = 0 9 + 17k = -8 + 0 9 + 17k = -8 Add '-9' to each side of the equation. 9 + -9 + 17k = -8 + -9 Combine like terms: 9 + -9 = 0 0 + 17k = -8 + -9 17k = -8 + -9 Combine like terms: -8 + -9 = -17 17k = -17 Divide each side by '17'. k = -1 Simplifying k = -1
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