How do you solve and write the following in interval notation: #-1 < x <5#?
Interval notation is a way of representing a subset of numbers on a number line.
The notation is as follows, where a and b are real numbers and a is the smaller value and b is the larger value:
If a number is included on the number line, you use a square bracket/parenthesis to represent it: [a,b]
If a number is not included on the number line, you use an round bracket/parenthesis to represent it: (a,b)
Sometimes, you can have one value that is included and one value that is not, so you can have an interval like: [a,b) (where a is included and b is not) or (a,b] (where a is not included but b is)
How do we know if a number is included if we are given an interval in set-builder notation (like the one in the question)?
Well, if we have a
If we have a
In the question, we have -1
To think about this in "words", this means that all values of x lie between the numbers -1 and 5 (but not inclusive of -1 and 5).