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📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 rac{x+3 - 4(x - 2)}{x - 2} = rac{x+3 - 4x + 8}{x - 2} = rac{-3x + 11}{x - 2}.

📌 So the inequality becomes:

📌 rac{-3x + 11}{x - 2} < 0.

📌 We analyze the sign of this rational expression by identifying the critical points where the numerator or denominator is zero:

📌 Numerator zero: $ -3x + 11 = 0 \Rightarrow x = rac{11}{3} $.

📌 Denominator zero: $ x - 2 = 0 \Rightarrow x = 2 $.

📌 These divide the real line into intervals:

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

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