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📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $ 7! = 5040 $

📌 $ 3! = 6 $, $ 2! = 2 $, so denominator = $ 6 imes 2 imes 2 = 24 $

📌 rac{5040}{24} = 210

📌 Thus, there are 210 distinct badge sequence orders.

📌 oxed{210}Question: Find all real numbers $ x $ such that $ rac{x+3}{x-2} < 4 $, where $ x

📌 Solution: We begin with the inequality:

📌 rac{x+3}{x-2} < 4, \quad x

📌 Subtract 4 from both sides to bring all terms to one side:

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