Question

Tìm x biết:
l 2 x - 3 l - x = l 2 - x l

 

Answer 1

\(\left|2x-3\right|-x=\left|2-x\right|\) 

TH1: \(\dfrac{3}{2}\le x\le2\)

\(\Rightarrow\left(2x-3\right)-x=2-x\)

\(\Leftrightarrow x-3=2-x\)

\(\Leftrightarrow2x=5\)

\(\Leftrightarrow x=\dfrac{5}{2}\left(ktm\right)\) 

TH2: \(x>2\) 

\(\Rightarrow\left(2x-3\right)-x=x-2\)

\(\Leftrightarrow x-3=x-2\)

\(\Leftrightarrow0=1\) (vô lý)  

TH3: \(x< \dfrac{3}{2}\) 

\(\Rightarrow\left(3-2x\right)-x=2-x\)

\(\Leftrightarrow3-3x=2-x\)

\(\Leftrightarrow3-2=-x+3x\)

\(\Leftrightarrow x=\dfrac{1}{2}\left(tm\right)\)

Vậy: ....