Explanation of the concept of unions in Precalculus/Algebra 2 (and vs or, etc)?

Question

When you have problems that involve a less than sign or a greater than sign, I know that it's crucial to express your answer in a certain way. I know it involves the concept of and vs or, and I know the U (and the upside down U) for union are involved. I apology for the lack of clarity of my question, but could someone give me some guidance here? Thanks!

...can someone please give me an answer that doesn't suck?

Answer 1

If you have a function where x<-5 and x >= 5, then x can be any number from -infinity to <-5.We show this by interval notation (- infinity, -5) where the parentheses mean - infinity and -5 are not included.

Now x can also be any number from 5 to +infinity We show this in interval notation as [5, + infinity) where the [ means the 5 is included.

So x can be (- infinity, -5) U [5, + infinity)

Answer 2

um if its a less than or less than or equal sign, you use and, if its greater than, greater than or equal, or equal, you use or. lol.