\(\left|x-2\right|=2x-3\)
Vì với mọi \(x\in Q\) ta luôn có \(\left|x\right|=\left|-x\right|\)
\(\Rightarrow\left[{}\begin{matrix}x-2=2x-3\\-\left(x-2\right)=2x-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3-2=2x-x\\-x+2=2x-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\3+2=2x+x\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\3x=5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=\frac{5}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{1;\frac{5}{3}\right\}\)
| x - 2| = 2x - 3
TH1: x - 2 = 2x - 3
=> 3 - 2 = 2x - x
=> x = 1
TH2: - (x - 2) = 2x - 3
=> -x + 2 = 2x - 3
=> 3 + 2 = 2x + x
=> 3x = 5
=> x = \(\frac{5}{3}\)
Vậy x ∈ \(\left\{1;\frac{5}{3}\right\}\)
Chúc bạn học tốt!
