Câu hỏi của Nguyễn Hoàng Hà

Question

Tìm x , biết

a, 2x-3>5x+10

b,2x²-3x>x+7x

c, (x-1).(x+3)<0

Mysterious Person · Accepted Answer

a) $2x-3>5x+10$ $\Leftrightarrow$ $2x-5x>10 +3\Leftrightarrow-3x>13\Leftrightarrow x< \dfrac{13}{-3}$ vậy $x< \dfrac{13}{-3}$

b) $2x^2-3x>x+7x$ $\Leftrightarrow$ $2x^2-3x-x-7x>0$

$\Leftrightarrow$ $2x^2-11x>0$ $\Leftrightarrow$ $x\left(2x-11\right)>0$ $\Leftrightarrow$ $\left\{{}\begin{matrix}x>0\2x-11>0\end{matrix}\right.$$\Leftrightarrow$ $\left\{{}\begin{matrix}x>0\x>\dfrac{11}{2}\end{matrix}\right.$

$\Rightarrow$ $x>\dfrac{11}{2}$ vậy $x>\dfrac{11}{2}$

c) $\left(x-1\right)\left(x+3\right)< 0$ $\Leftrightarrow$ $x^2+3x-x-3< 0$

$\Leftrightarrow$ $x^2+2x-3>0$ $\Leftrightarrow$ $x^2-x+3x-3>0$

$\Leftrightarrow$ $x\left(x-1\right)+3\left(x-1\right)$ $\Leftrightarrow$ $\left(x+3\right)\left(x-1\right)$

$\Leftrightarrow$ $\left\{{}\begin{matrix}x-1>0\x+3>0\end{matrix}\right.$$\Leftrightarrow$ $\left\{{}\begin{matrix}x>1\x>-3\end{matrix}\right.$ $\Rightarrow$ $x>1$ vậy $x>1$

Câu trả lời:

a) $2x-3>5x+10$ $\Leftrightarrow$ $2x-5x>10 +3\Leftrightarrow-3x>13\Leftrightarrow x< \dfrac{13}{-3}$ vậy $x< \dfrac{13}{-3}$

b) $2x^2-3x>x+7x$ $\Leftrightarrow$ $2x^2-3x-x-7x>0$

$\Leftrightarrow$ $2x^2-11x>0$ $\Leftrightarrow$ $x\left(2x-11\right)>0$ $\Leftrightarrow$ $\left\{{}\begin{matrix}x>0\2x-11>0\end{matrix}\right.$$\Leftrightarrow$ $\left\{{}\begin{matrix}x>0\x>\dfrac{11}{2}\end{matrix}\right.$

$\Rightarrow$ $x>\dfrac{11}{2}$ vậy $x>\dfrac{11}{2}$

c) $\left(x-1\right)\left(x+3\right)< 0$ $\Leftrightarrow$ $x^2+3x-x-3< 0$

$\Leftrightarrow$ $x^2+2x-3>0$ $\Leftrightarrow$ $x^2-x+3x-3>0$

$\Leftrightarrow$ $x\left(x-1\right)+3\left(x-1\right)$ $\Leftrightarrow$ $\left(x+3\right)\left(x-1\right)$

$\Leftrightarrow$ $\left\{{}\begin{matrix}x-1>0\x+3>0\end{matrix}\right.$$\Leftrightarrow$ $\left\{{}\begin{matrix}x>1\x>-3\end{matrix}\right.$ $\Rightarrow$ $x>1$ vậy $x>1$

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