rac{-3x + 11}{x - 2} < 0.
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- Write the left-hand side as a single rational expression:
- rac{x+3 - 4(x - 2)}{x - 2} = rac{x+3 - 4x + 8}{x - 2} = rac{-3x + 11}{x - 2}.
- So the inequality becomes:
- 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 $.
