Answer:
According to the theorem,
if [tex]|x|<a[/tex], then [tex]-a<x<a[/tex].
If [tex]|x|> a[/tex], then [tex]x<-a[/tex] or [tex]x>a[/tex]
So, in this case, we have to apply the second case.
[tex]|3x+2|>7[/tex]
Then, we have the following compound inequiality
[tex]3x+2<-7\\3x+2>7[/tex]
These inequalities represent the solution for the problem. If we solve both of them, we have
[tex]3x+2<-7\\3x<-7-2\\3x<-9\\x<\frac{-9}{3}\\ x<-3[/tex]
And,
[tex]3x+2>7\\3x>7-2\\x>\frac{5}{3}[/tex]
This means that the solution for the given inequality comprehend all number less than -3 and more than 5/3.
