[tex] \frac{x}{x+1} \geq 3\\ \\ \Rightarrow \frac{x}{x+1}-3\geq 0\\ \\ \Rightarrow \frac{x}{x+1}-\frac{3(x+1)}{x+1}\geq 0\\ \\ \frac{x-3(x+1)}{x+1}\geq 0\\ \\ \frac{x-3x-3}{x+1}\geq 0\\ \\ \frac{-2x-3}{x+1}\geq 0 \ |\cdot (-1)\\ \\ \frac{2x+3}{x+1}\leq 0\\ \\ Facem \ tabelul \ de \ semne:[/tex]
x | -∞ [tex]\frac{-3}{2}[/tex] -1 +∞
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2x+3 | ------------------0++++++++++++++++++++++++++
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x+1 |--------------------------------0+++++++++++++++++++
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[tex]\frac{2x+3}{x+1}[/tex] | ++++++++++++0----------- | ++++++++++++++++++
[tex] \frac{2x+3}{x+1}\leq 0 \Rightarrow x\in [-\frac{3}{2}; \ -1)[/tex]
