| x - 1 | + | x - 3 | = 6

Ta có: | x -1 | = x - 1 nếu x -1 >= 0 hay x >= 1 hoặc | x-1| = 1-x nếu x-1<0 hay x<1

|x-3| = x -3 nếu x - 3>=0 hay x >=3 hoặc |x-3| = 3-x nếu x-3 < 0 hay x <3

TH1: x < 1

1 - x + 3 -x =6

=> 4 - 2x = 6

=> 2x = -2

=> x = -1 (TM)

TH2: 1 <= x < 3

x - 1 + 3 -x = 6

=> 0x +2 = 6

=> 0x = 4 (Loại)

TH3: X>=3

x - 1 + x-3=6

=> 2x - 4 = 6

=> 2x = 10

=> x =5 (TM)

Vậy x = {-1, 5}

TH1 : x<1

\(\Rightarrow x-1+x-3=6\\ \Rightarrow2x-4=6\\ \Rightarrow2x=10\\ \Rightarrow x=5\left(loai\right)\)

TH2: \(1\le x\le3\)

\(\Rightarrow x-1-\left(x-3\right)=6\\ \Rightarrow0x+2=6\\ \Rightarrow0x=4\\ \Rightarrow x\in\varnothing\)

TH3:\(x>3\)

\(\left(x-1\right)+\left(x-3\right)=6\\ \Rightarrow2x-4=6\Rightarrow x=5\left(TM\right)\)

Vậy x=5