The first thing is to describe each interval on its own.
If you were to describe the left interval (x<-10) from left-to-right, you'd say, "It goes from negative infinity to -10, not including -10." To put that into interval notation, you'd have:
[tex]\big(-\infty, -10\big)[/tex]
The right interval (x>-2) would be described as "from -2 to infinity, not including -2." In interval notation, we'd write this as:
[tex]\big(-2, \infty \big)[/tex]
Now that we have each one individually, we need to glue them together to say, "You can pick a number from the left interval OR the right interval." The way we do this, the way we write "or" with intervals is with the union symbol: [tex]\cup[/tex]
[tex]\big(-\infty,-10 \big) \cup \big (-2,\infty\big)[/tex]
