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Combining two or more inequalities with the word and
or or
yields what is called a compound inequality.
| Compound Inequality | Is Read As |
|---|---|
| x < 5 or x > 8 | x is less than 5 or greater than 8. |
| x > 2 and x ≤ 4 | x is greater than 2 and less than or equal to 4. |
Compound inequalities using the word and
are commonly written without showing the actual word. Consider the following example.
x > 2 and x ≤ 4
The first inequality can be rewritten as 2 < x because the statement x is greater than 2
is equivalent to 2 is less than x.
With this change, the inequality can be rewritten as follows.
2 < x and x ≤ 4 ⇒ 2 < x ≤ 4
It is important to note that compound inequalities written with the variable between such symbols, similar to the given example are compound inequalities pertaining to and.