What is the term for an equation that represents a relationship between different quantities with one or more variables?

An equation that represents a relationship between different quantities with one or more variables is called an equation. Equations typically show how two expressions are equal to each other, often involving variables that can take on different values, which allows for a multitude of solutions depending on the values assigned to the variables.

For example, consider the equation (2x + 3 = 7). In this case, the equation expresses a specific relationship between the quantities involved: the quantity (2x + 3) equals (7). The variable (x) can represent various numbers, and solving the equation will lead to the value of (x) that satisfies this relationship.

While terms like expression, formula, and open sentence have specific meanings in mathematics, they do not capture the concept of a relationship defined by equality in the way that an equation does. An expression is a combination of numbers and variables without an equality sign, a formula typically provides a specific rule or calculation method, and an open sentence implies a statement that may not be true depending on the values of the variables involved. Thus, the correct term for an equation representing relationships between quantities is indeed an equation.