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

Oct 12, 2017

$x \in \left[12 , \infty\right)$ and $x \in \left(- \infty , - 4\right)$

#### Explanation:

Lets take your question as an example.

We have $x \ge 12$

This means the value of $x$ can be $12$ or greater than $12$ up to $\infty$.

So the interval notation for this will be $x \in \left[12 , \infty\right)$

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 $x \in \left[12 , \infty\right)$ we say that $x$ can be ranging from $12$ to $\infty$ where $12$ is included and $\infty$ 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 $x \in \left(- \infty , - 4\right)$

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