What does a variable represent in mathematics?

In mathematics, a variable is indeed a letter or a symbol that represents one or more numbers. It serves as a placeholder for values that can change or vary in mathematical expressions and equations. For instance, in the expression ( x + 5 = 10 ), the variable ( x ) can represent different numbers that satisfy the equation, specifically the number 5 in this case.

Variables are fundamental in algebra because they allow mathematicians and students to work with general cases rather than needing to specify particular values every time. This abstract representation is essential for formulating equations, solving problems, and exploring relationships between quantities.

Understanding this concept of a variable enables students to manipulate mathematical expressions and develop deeper insights into algebraic thinking. It sets the foundation for further topics in mathematics, including functions, equations, and statistics.