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
$+) -3\le \:x<-\dfrac{1}{2}\:\to x+3-\left(-\left(2x+1\right)\right)=x$
$\to x+3-\left(-\left(2x+1\right)\right)=x$
$\to 3-\left(-\left(2x+1\right)\right)=0$
$\to 3+2x+1=0$
$\to 2x+4=0$
$\to 2x=-4$
$\to x=-2$
$+) x\ge -\dfrac12$
$\to x+3-\left(2x+1\right)=x$
$\to 3-\left(2x+1\right)=0$
$\to -\left(2x+1\right)=-3$
$\to 2x+1=3$
$\to 2x=2$
$\to x=1$
