Ta có :
\(\left|x-1\right|=2x-5\)
Mà \(\left|x-1\right|\ge0\Leftrightarrow2x-5\ge0\)
\(\Leftrightarrow x-1=2x-5\)
\(\Leftrightarrow5-1=2x-x\)
\(\Leftrightarrow4=x\)\(\left(tm\right)\)
Vậy .................
\(\left|x-1\right|=2x-5\)
th1: \(x-1\ge0\Leftrightarrow x\ge1\)
\(\Rightarrow\left|x-1\right|=2x-5\Leftrightarrow x-1=2x-5\Leftrightarrow x=4\left(tmđk\right)\)
th2: \(x-1< 0\Leftrightarrow x< 1\)
\(\Rightarrow\left|x-1\right|=2x-5\Leftrightarrow1-x=2x-5\Leftrightarrow3x=6\Leftrightarrow x=2\left(loại\right)\)
vậy \(x=4\)
\(\left|x-1\right|=2x-5\)
Xét: \(x\ge1\)
\(\Rightarrow x-1=2x-5\)
\(\Rightarrow x=2x-4\)
\(\Rightarrow x=4\)
Xét: \(x< 1\)
\(-x+1=2x-5\)
\(\Rightarrow-x=2x-6\)
\(\Rightarrow2x-\left(-x\right)=6\)
\(3x=6\Rightarrow x=2\)
Không thỏa mãn đk:\(x< 1\) nên loại
