1. Feel that there are a lot of inequality relations in life, understand the meaning of inequality and linear inequality, and make students find the solution of inequality spontaneously by solving simple practical problems, which will correctly represent the solution set of inequality on the number axis;

2. Experience the process of establishing inequality model through concrete examples, explore the different meanings of inequality solutions and sets, and infiltrate the idea of combining numbers with shapes;

3. Through the exploration of inequality, inequality solution and solution set, guide students to actively participate in the discussion of mathematical problems on the basis of independent thinking, and cultivate their awareness of cooperation and communication; Let students fully realize that mathematics exists everywhere in life and can be applied to all fields of life.

Second, the knowledge framework.

Third, the key points

Understand and master the essence of inequality;

Correctly apply the properties of inequality;

Establishing equations to solve practical problems will solve the one-dimensional linear equation of "ax+b=cx+d";

Find the inequality relationship in practical problems and establish a mathematical model;

Solution sets and solutions of linear inequalities in one variable.

Fourth, difficulties.

Understanding of solution set of one-dimensional linear inequality system:

Find out the thinking method of solving practical problems with column inequalities and solve unary linear inequalities with brackets;

Correctly understand the meaning of inequality, inequality solution and solution set, and correctly express the solution set of inequality on the number axis.

Verb (abbreviation of verb) summary of knowledge points and concepts

1. Inequality: Formulas that express the relationship between size with symbols "",≤ "and ≥" are called inequalities.

2. Classification of inequalities: Inequalities are divided into strict inequalities and non-strict inequalities.

Generally speaking, connected inequalities using pure greater than signs and less than signs ">" and "< are called strict inequalities, and inequalities connected by not less than signs (greater than or equal to signs), not greater than signs (less than or equal to signs)," ≥ "and" ≤ "are called non-strict inequalities or generalized inequalities.

3. Solution of inequality: The value of the unknown quantity that makes inequality valid is called the solution of inequality.

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

5. Representation method of inequality solution set;

(1) is expressed by inequality: generally, an inequality with unknowns has countless solutions, and its solution set is a range, which can be expressed by the simplest inequality. For example, the solution set of x- 1≤2 is x≤3.

(2) Expressed on the number axis: The solution set of inequality can be intuitively expressed on the number axis, which vividly shows that inequality has infinite solutions. Two points should be paid attention to when expressing the solution set of inequality with the number axis: first, the boundary line should be fixed; The second is to set the direction.

6. Some of the same problem-solving principles that can be followed when solving inequalities.

(1) inequality F(x) G(x) and inequality G(x)>F(x) homogeneous solution.

(2) If the inequality f (x)

(3) If the domain of inequality F(x) G(x) is included in the domain of analytic formula H (x), and H(x) >; 0, then the inequality f (x)

7. The nature of inequality:

(1) If x >；; Y, then YY; (symmetry)

(2) If x>y, y & gtz；; Then x & gtz；; (transitivity)

(3) if x>y and z is any real number or algebraic expression, then x+z >; y+z； (plus rule)

(4) If x>y, z>0, then xz & gtyz；; If x>y, z<0, and then xz.

(5) if x>y, z>0, then x ÷ z >; y \u z； If x>y, z<0, and then x \z

(6) If x>y, m>n, then X+M > Y+n (sufficient and unnecessary conditions)

(7) If x>y>0, m>n>0, then xm & gtyn

(8) if x>y>0, then the n power of x >; The n power of y (n is a positive number)

8. One-dimensional linear inequality: the left and right sides of the inequality are algebraic expressions with only one unknown number, and the degree of the unknown number is 1. Inequalities like this are called one-dimensional linear inequalities.

9. The general order of solving one-dimensional linear inequality:

(1) denominator (using inequality properties 2 and 3)

(2) Dismantle the bracket

(3) Shift term (using inequality property 1)

(4) merging similar projects

(5) Transform the unknown coefficient into 1 (using inequality properties 2 and 3).

(6) Sometimes it is necessary to express the solution set of inequality on the number axis.

10. Comprehensive application of linear inequality and linear function;

Generally, the function expression is obtained first, and then the inequality is simplified.

1 1. One-dimensional linear inequality group: Generally speaking, it is a combination of several one-dimensional linear inequalities about the same unknown quantity.

A set of one-dimensional linear inequalities is established.

12. Steps to solve a set of linear inequalities:

(1) Find the solution set of each inequality;

(2) Find the common part of each inequality solution set; (Generally, several axes are used)

(3) The public part is expressed in algebraic symbolic language. (it can also be said that it is a conclusion)

13. tips for solving inequality

(1) is greater than the maximum (much larger);

For example: X>- 1, X>2. The solution set of the inequality group is X>2.

(2) less than the minimum (small and small);

For example: x

(3) Crossing the middle is greater than or less than;

(4) There is no solution to the part that is not disclosed;

14. Formulas for solving inequality groups

(1) Maximize the same size.

For example, the solution set of x>2, x>3. Inequality group is X>3.

(2) Take the small as the big.

For example, x

(3) Find the middle between big and small.

For example, x 1, the solution set of inequality group is 1.

(4) Keep the change, more or less.

For example, x3, the inequality group has no solution.

15. Steps to solve practical problems by applying inequality groups

(1) Check the meaning of the problem

(2) Set unknowns, and list inequality groups according to the set unknowns.

(3) Solving inequality groups

(4) The solutions of practical problems are established by the solutions of inequality groups.

(5) Answer

16. Solving practical problems with inequality groups: its general solution is not necessarily the solution of practical problems, but should be combined with concrete analysis of real life to finally determine the result.