Question

Раскройте модуль, если $\alpha \leq -3$: |$\alpha$ + 4|

Answer 1

Ответ:

$\alpha \leq -3\ \ \ \Rightarrow \ \ \ \alpha +3\leq -3+3\ \ ,\ \ \ \alpha +3\leq 0\ \ ,\\\\(\alpha +3)+1\leq 0+1\ \ \Rightarrow \ \ \ \alpha +4\leq 1\\\\a)\ \ 0\leq \alpha +4\leq 1\ \ \to \ \ \ |\, \alpha +4|=\alpha +4\ \ ,\ \ -4\leq \alpha \leq -3\\\\b)\ \ \alpha +4<0\ \ \to \ \ \ |\, \alpha +4|=-\alpha -4\ \ ,\ \ \alpha <-4\\\\\\|\alpha +4|=\left\{\begin{array}{l}\alpha +4\ ,\ esli\ \ \alpha \in [-4\ ;-3\ ]\\-\alpha -4\ ,\ esli\ \alpha \in (-\infty;-4\, )\end{array}\right$