1. equation: first, let letters represent unknowns, and then write an equation containing unknowns according to the equation relationship, which is called an equation.

2. One-dimensional linear equation

One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions, which is called one-dimensional linear equation. Finding the value of the unknown quantity in the equation is called the solution of the equation.

(3) Properties of the equation

① Adding (or subtracting) the same algebraic expression on both sides of the equation is still valid.

If a=b

Then a+c=b+c

② Both sides of the equation are multiplied or divided by the same non-zero algebraic expression at the same time, and the equation still holds.

If a=b

Then there is a c = b c or a \c = b \c(c≠0).

③ The equation is transitive.

If a 1 = a2, a2 = a3, a3 = a4, ... an = an, then a 1 = a2 = a3 = a4 =...= an.

3. Steps to solve the equation

The steps to solve a linear equation with one variable are: removing denominator, brackets, shift terms, merging similar terms, and converting unknown coefficients into 1.

(1) Denominator: Turn the coefficient into an integer.

(2) stent removal

③ Shift term: shift the sign of an item on one side of the equation to the other side.

④ Merge similar items.

⑤ The coefficient is 1.

2 rational number knowledge points

1. Numbers greater than 0 are called positive numbers.

2. Numbers with negative sign "-"in front of positive numbers are called negative numbers.

3. Integers and fractions are collectively called rational numbers.

People usually use points on a straight line to represent numbers. This straight line is called the number axis.

Take any point on the straight line to represent the number 0, and this point is called the origin.

6. Usually, the distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A. ..

7. According to the definition of absolute value:

The absolute value of a positive number is itself;

The absolute value of a negative number is its reciprocal;

The absolute value of 0 is 0.

8. Positive numbers are greater than 0, 0 is greater than negative numbers, and positive numbers are greater than negative numbers.

9. Two negative numbers, the larger one has the smaller absolute value.

10. rational number addition rule:

(1) Add two numbers with the same sign, take the same sign, and add the absolute values.

(2) Add two numbers with different absolute values, take the negative sign of the addend with larger absolute value, subtract the number with smaller absolute value from the number with larger absolute value, and add the two numbers with opposite numbers to get 0.

(3) When a number is added to 0, the number is still obtained.

1 1. In rational number addition, two numbers are added, the position of the addend is exchanged, and the sum is unchanged.

12. In rational number addition, when three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged.

13. rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.

14. rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.

15. There is also a rational number: two numbers whose product is 1 are reciprocal.

16. In general rational number multiplication, two numbers are multiplied, and the exchange factor and product are in the same position.

17. Multiply three numbers, first multiply the first two numbers, or multiply the last two numbers, and the products are equal.

18. Generally speaking, a number multiplied by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and then adding the products.

19. rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.

20. Divide two numbers, the same sign is positive, and the different sign is negative, divided by the absolute value. Divide 0 by any number that is not equal to 0 to get 0.

3 Unequal and unequal groups

Solution set of 1. inequality: All solutions of an unknown inequality constitute the solution set of this inequality.

2. One-dimensional linear inequality: the left and right sides of the inequality are algebraic expressions, and there is only one unknown, and the highest order of the unknown is 1. Inequalities like this are called one-dimensional linear inequalities.

3. One-dimensional linear inequality group: Generally, several one-dimensional linear inequalities about the same unknown quantity are combined to form a one-dimensional linear inequality group.

4. Solution set of one-dimensional linear inequality group: The common part of the solution set of each inequality in one-dimensional linear inequality group is called the solution set of this one-dimensional linear inequality group.

5. The essence of inequality:

The basic property of inequality is 1: add (or subtract) the same number (or formula) on both sides of inequality, and the direction of inequality remains unchanged.

The basic property of inequality 2: both sides of inequality are multiplied (or divided) by the same positive number, and the direction of inequality remains unchanged.

The basic property of inequality 3: when both sides of inequality are multiplied (or divided) by the same negative number, the direction of inequality changes.

4 Important knowledge points of algebraic expressions

1. Algebraic expression: Algebraic expression is a general term for monomials and polynomials.

2. Algebraic expression addition and subtraction

Algebraic expression addition and subtraction operation, if you encounter parentheses, first remove the parentheses, and then merge similar items.

(1) bracket removal: add and subtract several algebraic expressions. If there are brackets, remove them first, and then merge similar items.

If the factor outside the brackets is positive, the symbols in the original brackets are the same after the brackets are removed.

If the factor outside the bracket is negative, the sign in the original bracket is opposite after the bracket is removed.

(2) Merge similar items:

After merging similar items, the coefficients of the obtained items are the sum of the coefficients before merging, and the letter part remains unchanged.

3. Monomial: An algebraic expression composed of the product of numbers or letters is called a monomial, and a single number or letter is also called a monomial.

4. Polynomials: Algebraic expressions composed of several monomials are called polynomials.

5. A power with the same radix refers to a power with the same radix.

6. Power with the same base: power with the same base, the base is unchanged, and the index is added.

7. Power Law: Power, constant cardinal number, exponential multiplication.

8. Power of product: the power of product. First, multiply each factor in the product separately, and then multiply the obtained power.

9. Multiply the monomial with the monomial

Multiply the monomial with the monomial, and multiply them by their coefficients and the same base respectively. For letters contained only in the monomial, they are used as a factor of the product together with its index.

10. Multiplication of monomial and polynomial

Multiplying a polynomial by a monomial is to multiply each term of a polynomial by a monomial, and then add the products.

1 1. Polynomial times polynomial

Multiply polynomials by multiplying each term of one polynomial by each term of another polynomial, and then add the products.

12. Division with the same base: division with the same base, constant base and exponential subtraction.

13. The monomial is divided by the monomial: the monomial is divided by the coefficient and same base powers respectively as the factor of the quotient; For the letter only contained in the division formula, it is used as the factor of quotient together with its index.

14. Polynomial divided by monomial: Polynomial divided by monomial, first divide each term of polynomial by this monomial, and then add the obtained quotients.