"First-degree Inequalities of One Variable" PPT courseware

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"First-degree Inequalities of One Variable" PPT courseware

Debate

(1)x

(2) If -5a<-5b, then a

(3) If -a>-b, then 2-a>2-b; ( )

(4) If a>b, then ac2>bc2; ( )

(5) If ac2>bc2, then a>b; ( )

(6) If a>0, and (b-1)a<0, then b>1. ( )

Do it

1. If m>n, and am

A． a>0 B． a<0 C． a=0 D． a0

2. If k<0, then which of the following inequalities is not true ()

A.k+2>k-2 B.-6k>0 C.k>-k D.k<-k

3. Use “＜” or “＞” to fill in the blanks:

(1)a__a+1 (2)a+2__a-2 (3)1-a__-a (4)a2__0(a≠0)

Review the past and learn the new

The solution to the equation x+4=0 is

The solution of the equation is x=-4 the value of the unknown

Make the left and right sides of an equation equal or make the equation true

If an inequality contains an unknown number, we call the value of the unknown number that makes the inequality true the solution of the inequality.

Give a verdict

Which of the following numbers are solutions to the inequality 2/3x>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?

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. Write the solution set of the inequality directly:

⑴ x+2>6 ⑵ 3x>9 ⑶ x－3>0

Solution: ⑴ x>4; ⑵ x>3; ⑶ x>3

Represent the solution set of the inequality on the number line

How can you express the solution set of the inequality x≥1 on the number line?

If it is larger, draw it to the right, if it is smaller, draw it to the left;

If there is an equal sign, draw a solid dot, if there is no equal sign, draw an open circle. As shown below

⑴ x>-1; ⑵ x≥-1; ⑶ x<-1; ⑷ x≤-1.

Summary: ① Steps to use the number line to represent the solution set of the inequality:

The first step: draw the number line; the second step: determine the boundary points; the third step: determine the direction.

②Use the number axis to represent the solution set of the inequality, and you should remember the following rules:

Draw a solid point if there is an equal sign (≥, ≤), and draw an open circle if there is no equal sign (>, <).

If it is larger, draw it to the right, if it is smaller, draw it to the left;

Expand and extend

1. The non-positive integer solution of the inequality x ≥ -4 is _______.

2. Represent the solution set of the inequality x>-3.5 on the number line, and write all the negative integer solutions of this inequality.

3. Write an inequality with three positive integer solutions

Example List the inequalities based on the following statements.

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

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

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

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

(5)a is a non-positive number; a≤0

(6) The sum of a and 5 is less than 7; a+5<7

1.Judge right or wrong:

(1) The inequality x-1>0 has countless solutions;

(2) The solution set of the inequality 2x-3≤0 is x≥2/3

2. Among 0, -4, 3, -3, 1/5, -5, 4, -10.

___________ is the solution to the equation x+4=0.

___________ is the solution to the inequality x+4≥0

___________ is the solution to the inequality x+4<0

3. The positive integers that satisfy the inequality x-1<4 are ( )

A, 1, 2, 3, 4 B, 0, 1, 2, 3, 4

C, 0, 1, 2, 3 D, infinite

4. Which of the following statements is correct ( )

A． There is 1 solution to the inequality 2x≥3.

B． The solution set of the inequality x + 1<3 is x<3

C. The solution set of inequality 3x≥6 is x≥2

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Update Time: 2024-06-24

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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