Let's say a vector $u$ and its case is $(m+n)u= mu+nu$. if $m>0$ and $n<0$ then would its magnitude be $(|m| + |n|)|u|$? Then if $7u-4u$ are the case then would its magnitude still be $11u$ (by adding modulas of $7u$ and $-4u$)?
Ultimately is it right that magnitude of $(7u - 4u)$ is $(|7| + |-4|)|u|$?
Say $u$ is a two-dimensional vector in Euclidean space. Then $|u|$ is defined as $$|u|=\sqrt{u_x^2+u_y^2}.$$ If we multiply $u$ with a scalar $c$ we will get a length of
$$|cu|=\sqrt{c^2u_x^2+c^2u_y^2}=|c||u|.$$
If $c=a+b$, this does not change, i.e., we have $|a+b||u|$, but we cannot reduce $|a+b|$ to $|a|+|b|.$ For instance, take your numbers, $a=7,b=-4$. Then we have $$|a+b|=|7-4|=|3|=3$$ and $$|a|+|b|=|7|+|-4|=7+4=11,$$
which are not equal.