The nature of the equation, the fundamental properties of the equation

An equation with unknowns is called an equation.

The basic property of the equation 1: the same number or the same algebraic formula is added or subtracted from both sides of the equation at the same time, and the result is still the equation.

It is expressed by letters as: if a b, c is a number or an algebraic formula. Then:

1〕a+c＝b+c

2〕a-c＝b-c

Basic property of equation 2: The result of multiplying or dividing both sides of the equation by the same non-zero number is still an equation.

3 If a=b, then b=a (symmetry of the equation).

4 If a = b, b = c then a = c (transitivity of the equation) equation: an equation with unknowns is called an equation.

The solution of the equation: The value of the unknown that equalizes the left and right sides of the equation is called the solution of the equation.

Solving Equations: The process of finding the solution of an equation is called solving an equation.

Shift: Shifting certain terms in an equation from one side of the equation to the other after changing their sign, this deformation is called shifting, according to the fundamental properties of the equation1.

The basic properties of the equation are as follows:

1. The equation obtained by adding or subtracting the same number or the same equation on both sides of the equation is the same solution as the original equation.

2. The equation obtained by multiplying or dividing by the same non-0 number on both sides of the equation is the same solution as the original equation.

An equation is an equation that contains unknowns.

It is an equation that expresses the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, operations), and the value of the unknown number that makes the equation true is called the "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

By solving the equation, you can avoid the need to think backwards, and directly list the equations containing the quantities you want to solve. Equations come in many forms, such as unary linear equations.

Binary Quadratic Equation, a Hunger Quadratic Equation.

and so on, you can also form a system of equations to solve multiple unknowns.

In mathematics, an equation is a statement that contains an equation of one or more variables. Solving the equation involves determining which values of the variable make the equation true. Variables are also known as unknowns, and the value of the unknowns that satisfies equality is called the solution of the equation.

As early as 3,600 years ago, the ancient Egyptians wrote mathematical problems on papyrus paper that involved equations with unknowns.

Around 825 A.D., Central Asia.

Mathematician Al Khorazmi.

He once wrote a book called "Elimination and Reduction".

focuses on the solution of equations.

The basic properties of the equation are as follows: (1) The same number or the same integer is added (or subtracted) to both sides of the equation.

The resulting equation has a common solution with the original equation (called the same solution equation excitation.

2) If both sides of the equation are multiplied (or divided) by the same number that is not equal to zero, the resulting equation and the original square segment are the same solution equation grip state. The fundamental properties of equations are the basis for solving equations.

Solving an equation is actually the process of turning a relatively complex equation into a simple equation according to the basic properties of the equation. The resulting x=a is also the same solution of the original equation. So a is the solution of the original equation.

In elementary school, limited to the knowledge base of students, the solution of equations is not based on the basic properties of equations, but according to the inverse operation relationship between addition and subtraction, multiplication and division. After proper practice, the rules of shifting terms are summarized in popular language such as "shifting, adding, changing, subtracting, and adding", so as to lay a little foundation for further learning numbers.

The definition of an equation refers to an equation with unknowns. It is an equation that expresses the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, operations), and the value of the unknown number that makes the equation true is called the "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

By solving the equation, you can avoid the difficulty of reverse thinking, and directly list the equation containing the quantity you want to solve. Equations have a variety of forms, such as unary linear equations, binary linear equations, unary quadratic equations, etc., and can also form a system of equations to solve multiple unknowns.

Methods for solving equations:

1. Denominator: Multiply both sides of the equation by the least common multiple of each denominator at the same time.

2. Remove brackets: Generally, first go to the small brackets, then go to the middle brackets, and finally go to the braces, but the order can sometimes be determined according to the situation to make the calculation simple, and the distribution law can be based on multiplication.

3. Shift terms: Move the terms containing unknown numbers in the equation to the other side of the equation, and don't forget to change the sign when moving the remaining items to the other side of the equation.

4. Merge similar terms: Convert the original equation into the form of ax=b(a≠0).

5. The coefficient is one: the coefficient of the two sides of the equation divided by the unknown number at the same time.

6. Derive the solution of the equation.

1. The equation of the equation is the reed:

There is a one-dimensional equation according to the elemental order.

A two-dimensional equation of difference, a cubic equation of one element, and a one-dimensional one-dimensional equation.

Binary quadratic equations, ternary quadratic equations, and multivariate multiple equations.

There are also fractional equations, polar equations, irrational equations, trigonometric equations, etc.

2. Inequality equations.

An equation is an equation that contains unknownsIt is an equation that expresses the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, and operations), and the value of the unknown number that makes the equation true is called the "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

Equations containing equal signs are called equations, and equations can be divided into contradictory equations and conditional equations. Add (or subtract the same integer) on both sides of the equation at the same time, multiply or divide by the same non-0 integer on both sides of the equation at the same time, and the equation still holds, e.g. 1+2=3.

Unary Linear Equation Solution1. Remove the denominator: multiply by the least common multiple of each denominator on both sides of the equation.

2. Remove brackets: first go to the small brackets, then go to the middle brackets, and then go to the braces after the most socks.

3. Shift terms: move the terms containing unknowns to one side of the equation, and move the other terms to the other side of the equation; The move item needs to be renumbered.

4. Merge similar terms: Transform the equation into the form of ax=b(a≠0).

5. The coefficient is reduced to 1.

Summary. Hello dear,"5x＝10"It can be understood in the following ways: Multiplying x equals 10, the value of x is multiplied by 1 5 on both sides of the equation, 5x 5 = 10 5, and simplified to get x = will"5x＝10"It is called an equation and represents an unknown quantity x, satisfying 5 times x equals 10.

There are many ways to solve equations, including algebra, factorization, graphing, etc. 4. "5x＝10"It can also be represented as a proportion, where 5 and 10 are two numbers proportional, x is one of the unknowns, and 5x is its proportional part.

The value of x can be obtained by solving for the scale as 2.

Equation refers to an equation containing unknowns, which is an equation that expresses the equality relationship between two mathematical formulas (such as two suspicious hole numbers, celery or dry functions, quantities, and operations).

The value of the unknown that makes the equation true is called the "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

There are several ways to understand 5x 10.

Dear, hello, there is garbled in the words you sent.

Can you send me a **?

In the middle is the equals sign.

Hello dear,"5x＝10"It can be understood in the following ways: multiplying x equals 10, the value of x is multiplied by 1 5, 5x 5 = 10 5, and x = will"5x＝10"It is called an equation and represents an unknown quantity x, satisfying 5 times x equals 10. There are many ways to solve the slag program, including algebraic method, factorization method, graph method, etc.

4. "5x＝10"It can also be represented as a proportion, where 5 and 10 are two numbers proportional, x is one of the unknowns, and 5x is its proportional part. The value of x can be obtained by solving for the scale as 2.

I also have a way of understanding that 5 and x are multipliers and 10 is the product.

Dear, you are right in this way Ha <>

Can you think of this equation as a division operation when solving it?

It is not possible to do it with the nature of the equation.

It's okay to pro, just change the equation.

An equation containing an unknown number is called an equation Equation Fundamental Property 1: Both sides of the equation are added or subtracted from the same number or the same algebraic equation at the same time.

The result is still expressed in letters as: canonical kiroa a b, c is a number or an algebraic formula. Then:

1 a+c b+c 2 a-c b-c The basic property of the equation 2: The result obtained by multiplying or dividing both sides of the equation by the same non-0 number is still equation 3 If a = b, then b = a (symmetry of the equation) 4 If a = b, b = c then take care of a = c (transitivity of the equation) equation: the equation containing unknowns is called the equation The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation

The process of finding the solution of an equation is called solving the equation shift: after changing the sign of some term in the equation, it moves from one side of the equation to the other, and this deformation is called shifting, according to the basic property of the equation 1