Алгебра 7 класс

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

Elementary algebra is a section of algebra that studies the most basic concepts. It is usually studied after mastering the fundamental concepts of arithmetic. Arithmetic deals with numbers and simple operations (+, −, ×, ÷) performed on them. In algebra, numbers are replaced by variables (a, b, c, x, y, and so on). This approach is useful because:

• It allows for a general understanding of the laws of arithmetic (for example, a+b=b+a for any a and b), which is the first step towards a systematic study of the properties of real numbers.
• It introduces the concept of the "unknown," formulates equations, and explores methods to solve them. For example, "Find the number x such that 3x + 1 = 10" or, in a more general case, "Find the number x such that ax + b = c." This leads to the conclusion that determining the value of a variable lies not in the nature of the numbers in the equation but in the operations between them.
• It formulates the concept of function. For instance, "If you sell x tickets, your profit will be 3x − 10 rubles, or f(x) = 3x − 10, where f is the function and x is the number on which the function depends."