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.