Question

How do you solve and write the following in interval notation: `| 5x + 3 | >18`?

Answer 1

When you have the absolute value, you can remove it considering the two sign `\pm`. You have to be careful with the inequality because the `+` keep the direction of the inequality while the `-` inverte it.
In your case you have

`|5x+3|>18`

`5x+3>18` and `5x+3<-18`

`5x>15` and `5x<-21`

`x>3` and `x<-21/5`.

As interval you can say that `x in (-oo, -21/5) and (3, +oo)`.