Question

|x-1|=2X+3

 

Answer 1

|x-1|=2x+3

 \(\Leftrightarrow\left[{}\begin{matrix}x-1=2x+3\\x-1=-2x-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\3x=-2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{-2}{3}\end{matrix}\right.\)

Answer 2

`x-1=|2x+3|(x>=1)`
`<=>` $\left[ \begin{array}{l}x-1=2x+3\\1-x=2x+3\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x=-4(l)\\3x=-2\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x=-4(l)\\x=-\dfrac23(l)\end{array} \right.$
Vậy pt vô nghiệm

 

Answer 3

       \(\left|x-1\right|=2x+3\)

<=> \(\left[{}\begin{matrix}x-1=2x+3\left(x\ge1\right)\\1-x=2x+3\left(x< 1\right)\end{matrix}\right.\) 

<=> \(\left[{}\begin{matrix}x=-4\left(l\right)\\x=\dfrac{-2}{3}\left(tm\right)\end{matrix}\right.\)

Vậy nghiệm của phương trình là \(S=\left\{\dfrac{-2}{3}\right\}\)