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Simplifying 9(2k + 3) + 2 = 11(k + -5) Reorder the terms: 9(3 + 2k) + 2 = 11(k + -5) (3 * 9 + 2k * 9) + 2 = 11(k + -5) (27 + 18k) + 2 = 11(k + -5) Reorder the terms: 27 + 2 + 18k = 11(k + -5) Combine like terms: 27 + 2 = 29 29 + 18k = 11(k + -5) Reorder the terms: 29 + 18k = 11(-5 + k) 29 + 18k = (-5 * 11 + k * 11) 29 + 18k = (-55 + 11k) Solving 29 + 18k = -55 + 11k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11k' to each side of the equation. 29 + 18k + -11k = -55 + 11k + -11k Combine like terms: 18k + -11k = 7k 29 + 7k = -55 + 11k + -11k Combine like terms: 11k + -11k = 0 29 + 7k = -55 + 0 29 + 7k = -55 Add '-29' to each side of the equation. 29 + -29 + 7k = -55 + -29 Combine like terms: 29 + -29 = 0 0 + 7k = -55 + -29 7k = -55 + -29 Combine like terms: -55 + -29 = -84 7k = -84 Divide each side by '7'. k = -12 Simplifying k = -12
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