Question

How do you solve and write the following in interval notation: `x>=12` or `x<-4`?

Answer 1

`x in[12,oo)` and `x in(-oo,-4)`

Explanation:

Lets take your question as an example.

We have `x>=12`

This means the value of `x` can be `12` or greater than `12` up to `oo`.

So the interval notation for this will be `x in [12,oo)`

Here, this [ ] bracket means its a closed interval. This means `x` will include all the values in the bracket.
( ) bracket means an open interval, `x` will include the values in the bracket other than the ones on the extreme ends.

So when we write `x in [12,oo)` we say that `x` can be ranging from `12` to `oo` where `12` is included and `oo` is not.

Similarly `x<-4` says `x` has to be less than `-4` and cannot be greater than or equal to `-4` . In interval notation
It can be written as `x in(-oo,-4)`

Its an open interval on both sides because `x` can be all the values in between `-oo` and `-4` but cannot be `-oo` or `-4`