Question

tìm x biết:|2x+3|=x+2

Answer 1

\(\left|2x+3\right|=x+2\left(đk:x\ge-2\right)\)

\(\Rightarrow\left[{}\begin{matrix}2x+3=x+2\left(x\ge-\dfrac{3}{2}\right)\\2x+3=-x-2\left(-2\le x< -\dfrac{2}{3}\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-1\left(tm\right)\\x=-\dfrac{5}{3}\left(tm\right)\end{matrix}\right.\)

Answer 2

\(\left|2x+3\right|=x+2\\ \Leftrightarrow\left[{}\begin{matrix}x+2=2x+3\\x+2=-2x-3\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-x=2-3\\x+2x=-3-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\3x=-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{5}{3}\end{matrix}\right.\)

Vậy x= -1 hoặc x= -5/3

Answer 3

Ta có : \(x+2\ge0\Leftrightarrow x\ge-2\)

+ Nếu \(x\ge\dfrac{-3}{2}\Rightarrow\left|2x+3\right|=x+2\Rightarrow2x+3=x+2\Rightarrow x=-1\left(TM\right)\)

+ Nếu \(-2\le x< \dfrac{-3}{2}\Rightarrow\left|2x+3\right|=x+2\Rightarrow-2x-3=x+2\Rightarrow x=\dfrac{-5}{3}\left(TM\right)\)

+Nếu \(-2>x\) Không có gt của x thỏa mãn