Question

tìm x biết : |x-1|=2x-5

Answer 1

\(|x-1|=2x-5\)

\(\Rightarrow\hept{\begin{cases}x-1=2x-5\\x-1=5-2x\end{cases}}\)khi\(\hept{\begin{cases}x\ge1\\x\le1\end{cases}}\)

TH1: x\(\ge\)1

\(\Rightarrow x-1=2x-5\)

\(\Rightarrow x-2x=-5+1\)

\(\Rightarrow-x=-4\Rightarrow x=4\left(tm\right)\)

TH2 : x\(\le\)1

\(\Rightarrow x-1=5-2x\)

\(\Rightarrow x+2x=5+1\)

\(\Rightarrow3x=6\Rightarrow x=2\left(L\right)\)

Vậy x=4

Answer 2

Vì /x-1/ = 2x - 5 => x-1 = 2x-5 hoặc x-1 = -(2x-5)

Trường hợp 1:

x-1 = 2x-5

x-2x = -5 + 1

x.(1-2)= -4

-x = -4

=> x = 4

Trường hợp 2:

x -1 = -(2x - 5)

x -1 = -2x+5

x+2x = 5+1

3x = 6

x = 6:3

x=2

Vậy x = 4 hoặc x=2

Học tốt nha bn

Answer 3

\(|x-1|=2x-5\)

Ta có:\(|x-1|\ge0\Rightarrow2x-5\ge0\Rightarrow2x\ge5\Rightarrow x\ge\frac{5}{2}\)

\(TH1:x-1=2x-5\)

\(\Rightarrow-1+5=2x-x\)

\(\Rightarrow4=x\left(TM\right)\)

\(TH2:x-1=-\left(2x-5\right)\)

\(\Rightarrow x-1=-2x+5\)

\(\Rightarrow x+2x=1+5\)

\(\Rightarrow3x=6\Rightarrow x=2< \frac{5}{2}\left(KTM\right)\)

Vậy\(x=4\)