"Inequality" Inequality and Inequality Group PPT Courseware 3

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"Inequality" Inequality and Inequality Group PPT Courseware 3

Problems in life: such as height, weight, speed, etc., need to quantify the objects in order to communicate and judge. Not only do we need to learn and study the relationship of equal quantities, but we also need to learn and study the relationship of inequality.

take a look

Do you remember the seesaw that children played on? Have you ever wondered how it works? In fact, the seesaw works by constantly changing the weight comparison between the two ends.

Mathematics and life

Question 1: The teacher bought two Christmas gifts at a 20% discount and paid a total of 16 yuan. Do you know the price of each gift?

Use x to represent the price of the gift. From the meaning of the question, we get: 8/5x =16

Question 2: The teacher bought two Christmas gifts at a 20% discount and paid less than 16 yuan. Do you know the price of each gift?

Use x to represent the price of the gift. According to the meaning of the question, we get: 8/5x＜16 16/0.8 x＞2

Definition of inequality:

Expressions that use “＞” or “＜” to express large or small relationships are called inequalities.

Expressions using "≠" to express inequality relationships are also called inequalities.

Expressions that use "≥" or "≤" to express a relationship of magnitude are called inequalities.

"≥" is read as "greater than or equal to" or "not less than"

"≤" is pronounced as "less than or equal to" or "no greater than"

Example 2. Which of the following expressions are inequalities?

①a+b=b+a ② -3＞-5 ③ x≠1

④x+3＞6 ⑤ 2m≤n ⑥ 2x-3

⑦50/x＜2/3 ⑧ y+3≥3

Inequalities may or may not contain unknown numbers.

Solution: (2), (3), (4), (5), (7), (8) are inequalities.

I will do it

1. Express it as an inequality:

⑴ The sum of a and 1 is a positive number; a+1>0

⑵ The sum of 2 times y and 1 is less than 3; 2y+1<3

⑶ The sum of 3 times y and 2 times x is a non-negative number 3y+2x≥0

⑷ The product of x times 3 plus 2 is at most 5. 3x+2≤5

2. Use appropriate symbols to express the following relationships:

(1) The sum of x and 1 is a positive number

(2) The sum of 2 times y and 1 is greater than 3

(3) The sum of 1/3 of x and 2 times of x is a non-positive number

(4) 30� of the sum of c and 4 is not greater than -2

(5) The quotient of x divided by 2 plus 2 is at most 5

(6) The square of the sum of the numbers a and b cannot be greater than 3

Solution to the inequality:

We once learned that "the value of the unknown that makes both sides of the equation equal is the solution of the equation." Similarly, the value of the unknown that makes the inequality true is called the solution of the inequality.

think:

Determine which of the following numbers are solutions to the inequality x >50:

76,73,79,80,74,9,75.1,90,60,-5,0,101,1000.

Can you find other solutions to this inequality? How many solutions does this inequality have?

Solution set of inequalities

All solutions of an inequality containing unknown numbers form the solution set of this inequality.

Note: Are the solutions to inequalities the same as the set of solutions to inequalities?

Exercise: 3. Which of the following statements is correct ( )

A. x=3 is the solution of 2x>1

B. x=3 is the only solution to 2x>1

C. x=3 is not a solution to 2x>1

D. x=3 is the solution set of 2x>1

An inequality that contains an unknown number and the degree of the unknown number is 1 is called a linear inequality. The process of finding the solution set of the inequality is called solving the inequality.

Representation method of solution set of inequalities

The first one: express it with a formula (such as x>2), that is, using the simplest form of inequality (such as x>a or x

The second type: Use the number axis to mark a certain interval on the number axis, and the values ​​corresponding to the points are all solutions to the inequality.

Example 6. Directly figure out the solution set of the inequality:

⑴ x+2>6 ⑵ 3x>9 ⑶ x－3>0

Solution: ⑴ x>4; ⑵ x>3; ⑶ x>3.

Among the following values ​​-3, -2, -1, 0, 1, 2, 3, there are ( ) solutions to the inequality 2X>4

A.4 B.3 C.2 D.1

Use an inequality to express "The difference between 2 times a and -1 is greater than 2". The correct answer is ( )

A 2a-1＞-2 B 2a-(-1)＞2

C 2【a-(-1)】＞-2 D 2(a+1)＞-2

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Update Time: 2024-07-02

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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