1.4. Find all real numbers $x$ for which the equality

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

holds.
1.4. 1. method. In the case $x \geq 0$ we distinguish two possibilities: the first is $x=1+t, t>0$, and then our equation reduces to $2 t=0$, which has no solutions. The second possibility is $x=1-t, \quad 1$ z $t$ z 0. In this case, the given equation is equivalent to $3=3$. In this case, the solution is $0 \leq x \leq 1$. The case $x<0$ is considered similarly. The final solution is $-1 \leq x \leq 1$.