Algebra is a branch of mathematics that can be roughly described as a generalization and extension of arithmetic. The word "algebra" is also used in the names of various algebraic systems. In a broader sense, algebra is understood as a branch of mathematics devoted to the study of operations on elements of a set of arbitrary nature, generalizing the usual operations of addition and multiplication of numbers.

Elementary algebra is a branch of algebra that studies the most basic concepts. Usually studied after learning the basic concepts of arithmetic. In arithmetic, numbers and the simplest (+, -, ×, ÷) operations with them are studied. In algebra, numbers are replaced with variables (a, b, c, x, y, and so on). This approach is useful because:

Allows you to get a general idea of ​​the laws of arithmetic (for example, a + b = b + a for any a and b), which is the first step to a systematic study of the properties of real numbers.
Allows you to introduce the concept of "unknown", formulate equations and study ways to solve them. (For example, “Find a number x such that 3x + 1 = 10” or, more generally, “Find a number x such that ax + b = c.” This leads to the conclusion that finding the value of a variable is not in the nature of the numbers from the equation, and in the operations between them.)
Allows you to formulate the concept of a function. (For example, "If you sold x tickets, then your profit will be 3x - 10 rubles, or f (x) = 3x - 10, where f is a function and x is the number on which the function depends.")