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📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 We test the sign of $ rac{-3x + 11}{x - 2} $ in each interval:

📌 For $ x < 2 $, say $ x = 0 $: numerator $ -3(0) + 11 = 11 > 0 $, denominator $ 0 - 2 = -2 < 0 $ â negative.

📌 For $ 2 < x < rac{11}{3} $, say $ x = 3 $: numerator $ -9 + 11 = 2 > 0 $, denominator $ 1 > 0 $ â positive.

📌 For $ x > rac{11}{3} $, say $ x = 4 $: numerator $ -12 + 11 = -1 < 0 $, denominator $ 2 > 0 $ â negative.

📌 We want where the expression is **less than 0**, so the solution is where it is negative: $ (-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 x \in (-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 oxed{(-\infty, 2) \cup \left(rac{11}{3}, \infty

📌 Question: Let $ a, b, c $ be real numbers such that $ a + b + c = 0 $. Prove that $ a^3 + b^3 + c^3 = 3abc $.

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