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Simplifying 5(9k + 2) = 7(8 + 2k) Reorder the terms: 5(2 + 9k) = 7(8 + 2k) (2 * 5 + 9k * 5) = 7(8 + 2k) (10 + 45k) = 7(8 + 2k) 10 + 45k = (8 * 7 + 2k * 7) 10 + 45k = (56 + 14k) Solving 10 + 45k = 56 + 14k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14k' to each side of the equation. 10 + 45k + -14k = 56 + 14k + -14k Combine like terms: 45k + -14k = 31k 10 + 31k = 56 + 14k + -14k Combine like terms: 14k + -14k = 0 10 + 31k = 56 + 0 10 + 31k = 56 Add '-10' to each side of the equation. 10 + -10 + 31k = 56 + -10 Combine like terms: 10 + -10 = 0 0 + 31k = 56 + -10 31k = 56 + -10 Combine like terms: 56 + -10 = 46 31k = 46 Divide each side by '31'. k = 1.483870968 Simplifying k = 1.483870968
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