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should you workout when sick - NBX Soluciones

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 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:

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

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Case 1:** $ 3\theta = 2k\pi + 2\theta $
Subtract $ 2\theta $ from both sides:
\theta = 2k\pi
Within $ [0, 2\pi) $, the only solution is $ \theta = 0 $.
Case 2:** $ 3\theta = 2k\pi - 2\theta $
Add $ 2\theta $ to both sides:
5\theta = 2k\pi \quad \Rightarrow \quad \theta = \frac{2k\pi}{5}
We now find all values of $ k $ such that $ 0 \leq \frac{2k\pi}{5} < 2...
Dividing by $ 2\pi $:
\leq \frac{k}{5} < 1 \quad \Rightarrow \quad k = 0, 1, 2, 3, 4

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