An inequality is a mathematical statement that looks exactly like an equation except that the equals sign is replaced with one of the five inequality symbols.

≠ not equal to

< less than

≤ less than or equal to

> greater than

≥ greater than or equal to

Imagine two friends of ages 9 and 12. Each of the five inequality symbols can be used to write a statement about their ages, depending on which aspect about their ages is to be emphasized.

9 ≠ 12 says that 9 is not equal to 12

9 < 12 says that 9 is less than 12

9 ≤ 12 says that 9 is less than or equal to 12

12 > 9 says that 12 is greater than 9

12 ≥ 9 says that 12 is greater than or equal to 9

Notice that 9 < 12 and 12 > 9 are two ways to represent the same relationship; when the 9 and 12 are reversed, the inequality is also reversed.

The difference in meaning of "greater than" and "greater than or equal to" is subtle. For example, let a...