Answer:
The region where the inequality is valid is (x>-5) and (x<-9).
The graph is attached.
Step-by-step explanation:
We have a inequality and we have to determine the region in the xy-plane that inequality.
[tex]|x+7|-2>0\\\\|x+7|-2+2>0+2\\\\|x+7|>2[/tex]
We divide the inequality in two regions:
1) When (x+7)>0, we have:
[tex]x+7>2\\\\x+7-7>2-7\\\\x>-5[/tex]
2) When (x+7)<0, we have:
[tex]-(x+7)>2\\\\-x-7+7>2+7\\\\-x>9\\\\(-x)(-1)<9(-1)\\\\x<-9[/tex]
Then, the region where the inequality is valid is (x>-5) and (x<-9).
The graph is attached.
