Question

Giải phương trình:

I2x+1I - Ix-1I = 0

Answer 1

=>|2x+1|=|x-1|

=>2x+1=x-1 hoặc 2x+1=1-x

=>x=-2 hoặc x=0

Answer 2

`|2x+1|-|x-1|=0`

`<=>|2x+1|=|x-1|`

`<=>4x^2+4x+1=x^2-2x+1`

`<=>3x^2+6x=0`

`<=>3x(x+2)=0`

`<=>` $\left[\begin{matrix} x=0\\ x=-2\end{matrix}\right.$

Answer 3

\(\left|2x+1\right|-\left|x-1\right|=0\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}x-1=2x+1\\x-1=-\left(2x+1\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x-1=1\\3x-1=-1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x=2\\3x=0\end{matrix}\right.\) \(\Leftrightarrow x=\left[{}\begin{matrix}-2\\0\end{matrix}\right.\)