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5x + 3y = 45.00 \\ - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 rac{2x - 1}{x + 3} - 1 > 0 \Rightarrow rac{2x - 1 - (x + 3)}{x + 3} > 0 \Rightarrow rac{2x - 1 - x - 3}{x + 3} > 0 \Rightarrow rac{x - 4}{x + 3} > 0

📌 Now analyze the sign of \( rac{x - 4}{x + 3} \)

📌 Critical points: \( x = -3 \) (excluded), \( x = 4 \)

📌 Sign chart:

📌 For \( x < -3 \), say \( x = -4 \): \( rac{-4 - 4}{-4 + 3} = rac{-8}{-1} = 8 > 0 \) â positive

📌 For \( -3 < x < 4 \), say \( x = 0 \): \( rac{-4}{3} < 0 \) â negative

📌 For \( x > 4 \), say \( x = 5 \): \( rac{1}{8} > 0 \) â positive

📌 The expression is positive in \( (-\infty, -3) \) and \( (4, \infty) \)

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