Question

Which compound inequality can be used to solve the inequaliy |3x+2|>7

Answer 1

My vision seems to be failing me

Answer 2

According to the theorem,

if
`|x|<a`, then
`-a<x<a`.

If
`|x|> a`, then
`x<-a` or
`x>a`

So, in this case, we have to apply the second case.

`|3x+2|>7`

Then, we have the following compound inequiality

`3x+2<-7\\3x+2>7`

These inequalities represent the solution for the problem. If we solve both of them, we have

`3x+2<-7\\3x<-7-2\\3x<-9\\x<(-9)/(3)\\ x<-3`

And,

`3x+2>7\\3x>7-2\\x>(5)/(3)`

This means that the solution for the given inequality comprehend all number less than -3 and more than 5/3.