|x+3|-|2x+1|=x . Giúp mk nha mn

Đáp án: $x\in\{1,-2\}$

Giải thích các bước giải:

$|x+3|-|2x+1|=x$

$+) x<-3\to -\left(x+3\right)-\left(-\left(2x+1\right)\right)=x$

$\to -\left(x+3\right)+2x+1=x$

$\to x-2=x$

$\to -2=0\to$ vô lý $\to x<-3$ vô nghiệm

$+) -3\le \:x<-\dfrac{1}{2}\:\to x+3-\left(-\left(2x+1\right)\right)=x$

$\to x+3-\left(-\left(2x+1\right)\right)=x$

$\to 3-\left(-\left(2x+1\right)\right)=0$

$\to 3+2x+1=0$

$\to 2x+4=0$

$\to 2x=-4$

$\to x=-2$

$+) x\ge -\dfrac12$

$\to x+3-\left(2x+1\right)=x$

$\to 3-\left(2x+1\right)=0$

$\to -\left(2x+1\right)=-3$

$\to 2x+1=3$

$\to 2x=2$
$\to x=1$