Tìm x biết : 1..(3-x)(x+1) < 0 2..(3x- 1)(2x+ 4) lớn hơn hoặc bằng 0 3..x+5/x-1 <0 giúp em v s ajjjjjj

Đáp án:

1. `(3 – x)(x + 1) < 0`

<=> \(\left[ \begin{array}{l}3 – x > 0 ; x + 1 < 0\\3 – x < 0 ; x + 1 > 0\end{array} \right.\)  

<=> \(\left[ \begin{array}{l}x < 3 ; x < -1\\x > 3 ; x > -1\end{array} \right.\) 

<=> \(\left[ \begin{array}{l}x < -1\\x > 3\end{array} \right.\) 

2 . `(3x – 1)(2x + 4) ≥ 0`

<=> \(\left[ \begin{array}{l}3x – 1 > 0 ; 2x + 4 > 0\\3x – 1 < 0 ; 2x + 4 < 0\end{array} \right.\) 

<=> \(\left[ \begin{array}{l}x > 1/3 ; x > -2\\x < 1/3 ; x < -2\end{array} \right.\) 

<=> \(\left[ \begin{array}{l}x > 1/3\\x < -2\end{array} \right.\) 

3. `(x + 5)/(x – 1) < 0`

<=> \(\left[ \begin{array}{l}x + 5 > 0 ; x – 1 < 0\\x + 5 < 0 ; x – 1 > 0\end{array} \right.\) 

<=> \(\left[ \begin{array}{l}x > -5 ; x < 1\\x < -5 ; x > 1 < Loại >\end{array} \right.\) 

`<=> -5 < x < 1`

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