4. If the inequality about $x$
$$
|x+a|<|x|+|x+1|
$$

has the solution set $\mathbf{R}$, then the range of values for $a$ is
4. $00$.
It is easy to verify that when $0<a<1$, we always have
$|x+a|<\max \{|x|,|x+1|\}$.
In conclusion, the range of values for $a$ is $0<a<1$.