"Basic Properties of Inequalities" PPT download

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"Basic Properties of Inequalities" PPT download

Part One: Learning Objectives

Know the basic properties of inequalities and be able to use the basic properties of inequalities to transform inequalities.

[Learning Focus] The derivation process of the basic properties of inequalities.

[Learning Difficulties] Use the basic properties of inequalities to transform inequalities.

Pre-study requirements:

1. Teachers and friends ask each other about the relevant knowledge of this class;

2. Communicate your mastery of concepts, examples, textbook exercises, and confusion during self-study.

1. (1)5>3,

5+2 > 3+2, 5-2>3-

(2)-1<3,

-1+2<3+2, -1-3<3-3

If the same number or integer is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.

Through the above deformation, the rule you find is:

If both sides of the inequality are multiplied (or divided) by the same positive number, the direction of the inequality sign remains unchanged.

When both sides of an inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes.

Basic properties of inequalities PPT, part 2 content: mutual exploration

Research requirements:

1. Teachers and friends explain to each other the key points and difficulties of this lesson, exchange problem-solving ideas, and standardize problem-solving steps;

2. The mentors will explain the concepts and examples according to the standardized steps, and prepare the exercises for the blackboard demonstration, which will be reviewed by the mentors, and other mentors will supplement and correct errors.

Thinking questions

1. It is known that a < - 1, then the following inequality is wrong ( )

A. 4a < - 4

B. - 4a < 4

C, a + 2 <1

D. 2 – a > 3

2. Given x < y, which of the following inequalities are true?

(1) x – 3 < y – 3 (2) – 5 x < – 5 y

(3)-3 x +2<- 3 y + 2 (4)- 3 x + 2 > - 3y + 2

3. It is known that a>b, if a<0, then a2______ab; if a>0, then a2______ab.

Basic properties of inequalities PPT, the third part: layered improvement

Requirements: 1. Teachers and friends conduct oral or written exercises and try to complete extended questions;

2. Communicate collectively, revise answers, and share basic questions with classmates. The teacher provides guidance. Group discussions on difficult exercises and layered exercises.

1. Determine right or wrong and explain the reasons

(1)∵a < b ∴ a-b < b-b

(2)∵a < b ∴ a/2

(3) ∵a < b ∴ - 2a < -2b

(4) ∵-2a > 0 ∴ a > 0

(5) ∵-a < 0 ∴ 3a < 0

2. If a＜c＜0＜b, then the relationship between abc and 0 is ( )

A.abc＜0 B.abc=0

C.abc>0 D.Unable to determine.

3. If x>y, and a is a rational number, then xa²_____ya²;

4. From the inequality (m-1)x>m-1, we get x<1, then what conditions should m satisfy?

Basic properties of inequalities PPT, part 4 content: summary:

summary:

① When using the basic properties of inequalities for deformation, when both sides of the inequality are multiplied (or divided) by the same letter, the number the letters represent is the key to the problem, which determines whether to use basic properties 2 or 3 of the inequality. That is, the question of whether the inequality sign needs to change direction;

②When using the basic property 3 of inequality, you need to change two signs, one is the property sign, and the other is the inequality sign.

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