Question

Tìm x biết | x-2 | - | 1-2x | = 0

Answer 1

Ta có :\(|x-2|-|1-2x|=0\)

\(\Rightarrow|x-2|=|1-2x|\)

\(\Rightarrow\orbr{\begin{cases}x-2=1-2x\\x-2=2x-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=3\\x=-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)

Vậy \(x=1\)hoặc \(x=-1\)

Answer 2

\(\left|x-2\right|-\left|1-2x\right|=0\)

\(\Leftrightarrow\left|x-2\right|=\left|1-2x\right|\)Xet tung TH :

TH1 :  \(x-2=1-2x\Leftrightarrow3x=3\Leftrightarrow x=1\)

TH2 : \(x-2=-1+2x\Leftrightarrow-x=1\Leftrightarrow x=-1\)

Vay \(x=\left\{\pm1\right\}\)