A number is less than 24 or greater the 30. How do you write compound inequality that represents the possible values the number?

Dec 4, 2016

The values of $n$ are the empty or null set or $n = \left\{\emptyset\right\}$

Explanation:

First, let's call the number we are looking for $n$

Then, If a number is "less than 24" we can write this as:

$n < 24$

Also, if this number, $n$, is "greater than 30" we can write:

$n > 30$

We can flip this inequality around to get:

$30 < n$

Combining these two terms gives:

$30 < n < 24$

However, because 30 is not less than 24 the values of $n$ are the empty or null set or $n = \left\{\emptyset\right\}$