Question

Solutia inecuatiei : x supra x+1 mai mare sau egal cu 3.

Answer 1

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Answer 2

$\frac{x}{x+1} \geq 3\\ \\ \Rightarrow \frac{x}{x+1}-3\geq 0\\ \\ \Rightarrow \frac{x}{x+1}-\frac{3(x+1)}{x+1}\geq 0\\ \\ \frac{x-3(x+1)}{x+1}\geq 0\\ \\ \frac{x-3x-3}{x+1}\geq 0\\ \\ \frac{-2x-3}{x+1}\geq 0 \ |\cdot (-1)\\ \\ \frac{2x+3}{x+1}\leq 0\\ \\ Facem \ tabelul \ de \ semne:$

x       | -∞                 $\frac{-3}{2}$           -1                          +∞

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2x+3 | ------------------0++++++++++++++++++++++++++

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x+1    |--------------------------------0+++++++++++++++++++

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$\frac{2x+3}{x+1}$ | ++++++++++++0----------- | ++++++++++++++++++

$\frac{2x+3}{x+1}\leq 0 \Rightarrow x\in [-\frac{3}{2}; \ -1)$