You may want to review comparing numbers first.

Often, we want to say that a number is between two other numbers, say 3 and 5. You might be used to writing this like so: 3 < x < 5. Intervals are a quicker way to write it; you just write (3, 5). (Of course, 3 and 5 could be replaced with any other numbers, including negative numbers or fractions. But the lesser number always goes on the left.)

There are two other things you need to know. One is that, if instead of a ‘<’ sign you see a ‘≤’ sign, then you need to put a bracket (like ‘[’ or ‘]’) instead of a parenthesis (like ‘(’ or ‘)’). The other is that sometimes there's only one bound; for example, you might just want to say that 3 < x. In that case, you write (3, ∞). (The symbol ‘∞’ just means that bound doesn't exist.)

Here's a list of all the possibilities. Remember that 3 and 5 are just examples.

If you mean: Then write:
3 < x < 5 (3, 5)
3 ≤ x < 5 [3, 5)
3 < x ≤ 5 (3, 5]
3 ≤ x ≤ 5 [3, 5]
3 < x (3, ∞)
3 ≤ x [3, ∞)
x < 5 (−∞, 5)
x ≤ 5 (−∞, 5]

Note that, when the ∞ symbol is on the left, you put a negative sign in front of it. Also note that it always has a parenthesis next to it, never a bracket.