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Simplifying 10(3k + 10) = 2(9k + 11) Reorder the terms: 10(10 + 3k) = 2(9k + 11) (10 * 10 + 3k * 10) = 2(9k + 11) (100 + 30k) = 2(9k + 11) Reorder the terms: 100 + 30k = 2(11 + 9k) 100 + 30k = (11 * 2 + 9k * 2) 100 + 30k = (22 + 18k) Solving 100 + 30k = 22 + 18k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-18k' to each side of the equation. 100 + 30k + -18k = 22 + 18k + -18k Combine like terms: 30k + -18k = 12k 100 + 12k = 22 + 18k + -18k Combine like terms: 18k + -18k = 0 100 + 12k = 22 + 0 100 + 12k = 22 Add '-100' to each side of the equation. 100 + -100 + 12k = 22 + -100 Combine like terms: 100 + -100 = 0 0 + 12k = 22 + -100 12k = 22 + -100 Combine like terms: 22 + -100 = -78 12k = -78 Divide each side by '12'. k = -6.5 Simplifying k = -6.5
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