Question

giải các bất phương trình sau
a/ |2x-3| ≥5
b/ |3x-2|<x+3
​c/ |x+1|>2x-1

Answer 1

a) \(\Rightarrow\left[{}\begin{matrix}2x-3\ge5\\2x-3\le-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge4\\x\le-1\end{matrix}\right.\)

b)\(\Rightarrow\left[{}\begin{matrix}3x-2< x+3\\3x-2>-x-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x< 5\\4x>-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x< \frac{2}{5}\\x>-\frac{1}{4}\end{matrix}\right.\Leftrightarrow-\frac{1}{4}< x< \frac{2}{5}\)\(\)

c) \(\Rightarrow\left[{}\begin{matrix}x+1>2x-1\\x+1< 1-2x\end{matrix}\right.\Leftrightarrow}\left[{}\begin{matrix}-x>-2\\3x< 0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x>\frac{1}{2}\\x< 0\end{matrix}\right.\)xl máy tính ko thể vẽ đc !

Answer 2

c)\(\left[{}\begin{matrix}x+1>2x-1\\x+1< 1-2x\end{matrix}\right.\Leftrightarrow}\left[{}\begin{matrix}-x>-2\\3x< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>\frac{1}{2}\\x< 0\end{matrix}\right.\)