\(\left|x-1\right|+\left|x-3\right|=2x-1\)
+ TH1: \(x< 1.\)
\(\Leftrightarrow1-x+3-x=2x-1\)
\(\Rightarrow4-2x=2x-1\)
\(\Rightarrow4+1=2x+2x\)
\(\Rightarrow5=4x\)
\(\Rightarrow x=5:4\)
\(\Rightarrow x=\frac{5}{4}\left(KTM\right)\left(loại\right).\)
+ TH2: \(x\ge3.\)
\(\Leftrightarrow x-1+x-3=2x-1\)
\(\Rightarrow2x-4=2x-1\)
\(\Rightarrow2x-2x=\left(-1\right)+4\)
\(\Rightarrow0x=3\)
\(\Rightarrow x=3:0\)
\(\Rightarrow\) \(x\) không có giá trị (loại).
+ TH3: \(1< x\le3.\)
\(\Leftrightarrow x-1+3-x=2x-1\)
\(\Rightarrow2=2x-1\)
\(\Rightarrow2+1=2x\)
\(\Rightarrow3=2x\)
\(\Rightarrow x=3:2\)
\(\Rightarrow x=\frac{3}{2}\left(TM\right)\left(nhận\right).\)
Vậy \(x=\frac{3}{2}.\)
Chúc bạn học tốt!
