Question

tìm x : I 5x - 1 I - I x - 4 I = 0

Answer 1

`|5x-1|-|x-4|=0`

`<=>|5x-1|=|x-4|`

`+)5x-1=x-4`

`<=>4x=-3`

`<=>x=-3/4`

`+)5x-1=4-x`

`<=>6x=5`

`<=>x=5/6`

Vậy `S={-3/4,5/6}`

Answer 2

Giải:

\(\left|5x-1\right|-\left|x-4\right|=0\) 

\(\Rightarrow\left|5x-1\right|=\left|x-4\right|\) 

\(\Rightarrow\left[{}\begin{matrix}5x-1=x-4\\5x-1=4-x\end{matrix}\right.\) 

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{-3}{4}\\x=\dfrac{5}{6}\end{matrix}\right.\) 

Vậy \(x\in\left\{\dfrac{-3}{4};\dfrac{5}{6}\right\}\) 

Chúc bạn học tốt!