What do we call a mathematical sentence that indicates that two sides have different values?

A mathematical sentence that indicates that two sides have different values is known as an inequality. Inequalities are used to compare two quantities that are not equal, using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). For example, if you have the inequality 3 < 5, it states that 3 is less than 5, highlighting the difference in values.

In contrast, an equation signifies that two sides are equal, typically expressed using the equals sign (=). An expression does not contain an equality or inequality sign; it is simply a mathematical combination of numbers, variables, and operations. An identity is a special type of equation that is true for all values of the variable involved but does not deal with comparing sizes or values directly in the way that inequalities do. Therefore, the key distinction is that inequalities specifically focus on the notion of difference in values, confirming that one side is not equal to the other.