Giải phương trình sau: ${|}$${x-2}$${|}$${=}$${2x+4}$

Answer

Ta có:

`|x - 2|` $\geqslant$ `0`

`=> 2x + 4` $\geqslant$ `0`

`=> 2x` $\geqslant$ `-4`

`=> x` $\geqslant$ `-2` 

`=>` $\left[\begin{matrix} x - 2 = 2x + 4\\ x - 2 = -2x - 4\end{matrix}\right.$

`=>` $\left[\begin{matrix} x - 2x = 4 + 2\\ x + 2x = -4 + 2\end{matrix}\right.$

`=>` $\left[\begin{matrix} -x = 6\\ 3x = -2\end{matrix}\right.$

`=>` $\left[\begin{matrix} x = -6 \ \text{(KTM)}\\ x = \dfrac{-2}{3} \ \text{(TM)}\end{matrix}\right.$

Vậy `S = {{-2}/3}`