Question

How do you solve and write the following in interval notation: `-1 < x <5`?

Answer 1

(-1,5)

Explanation:

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 `<` or `>` sign, it means that the value is not included.

If we have a `<=` or `>=` sign, it means that the value is included.

In the question, we have -1`<`x`<`5 : this means that the interval points are not included, so we use the round parenthesis to write the interval in interval notation as:

(-1,5)

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).