Solve the equation:

$$
|x+1|-|x|+3|x-1|-2|x-2|=x+2
$$
Answer: $x=-2$ or $x \geq 2$. If $x \geq 2$, we get an identity. If $1 \leq x<2$, we get the equation $4 x=8$, which has no roots in this interval. If $0 \leq x<1$, we get the equation $-2 x=2$, which has no roots in this interval. If $-1 \leq x<0$, we get $0=2$, which is impossible. If $x<-1$, we get the root $x=-2$.