Question

Bài 1 : Giải bất phương trình :

a. \(\frac{1-4x}{12}< \frac{5-3x}{9}\)

b. \(\frac{x-1}{x-2}>0\)

c. \(\frac{x+9}{x-1}>5\)

d. \(\frac{-3+1}{2x+1}< -2\)

e. \(\left(x-1\right)\left(x+2\right)< \left(x+4\right)^2-4\)

Answer 1

a)

\(\frac{1-4x}{12}< \frac{5-3x}{9}\Rightarrow9-36x< 60-36x\)

\(\Rightarrow9< 60\)

=> \(\forall x\in R\)

b)

\(\frac{x-1}{x-2}>0\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\x-2>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>2\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x>2\\x< 1\end{matrix}\right.\)

x thỏa mãn là : x < 1 hoặc x >2

c) \(\frac{x+9}{x-1}>5\Rightarrow x+1-5\left(x-1\right)>0\Rightarrow x+1-5x+5>0\)

\(\Rightarrow6-4x>0\Rightarrow4x< 6\Rightarrow x< \frac{2}{3}\)

d) Tương tự câu c

e) \(\left(x-1\right)\left(x+2\right)< \left(x+4\right)^2-4\)

\(\Rightarrow x^2+x-2< x^2+8x+16-4\Rightarrow-7x-14< 0\)

\(\Rightarrow7x+14>0\Rightarrow x>-2\)