"Inequality" PPT courseware on inequalities and inequality groups

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"Inequality" PPT courseware on inequalities and inequality groups

think:

1. What is an equation?

An equation that expresses an equality relationship using an equal sign is called an equation

2. What is an inequality?

An expression that uses an inequality sign to express an inequality relationship is called an inequality.

Inequality signs include: ≥ ≤>< ≠

Apply new knowledge and experience success

1. Which of the following expressions are inequalities?

① -1�3 ② -x+2=4

③ 3x ≠ 4y ④ 6 � 2

⑤ 2x -3 ⑥ 2m � n

Example 1: Expressed by inequality:

⑴ The sum of a and 1 is a positive number;

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

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

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

Expressed as an inequality:

⑴ a is a positive number;

⑵ a is a non-positive number;

⑶ The sum of a and 5 is less than 7;

⑷ The difference between a and 2 is not less than -1;

Compare and discuss

① -x+2 = 4 ② -x+2 � 4

③ x－(－1) = 0 ④ x－(－1) �0

⑤ x+2= 2x ⑥ x+2≠ 2x

Consolidation exercises:

1. Which of the following expressions are linear inequalities of one variable?

(1)-3>-5 (2)x>1

(3) 2x+y<6 (4) 2-x<3x+5

(5) 3x+1=0 (6) 50/x＜2/3

2.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.

Determine which of the following numbers are solutions to the inequality 2x >50: 70, 60, -5, 0, 10, 20, 25.

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

3. 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: 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

Representation method of solution set of inequalities

The first one: express it with an equation (such as x>3), that is, using the simplest form of inequality (such as x>a or x

The second type: Use the number line to represent the solution set of the inequality.

Use the number line to represent the solution set of the following inequalities:

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:

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

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

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For more information about the PPT courseware "Inequalities, Inequalities and Groups of Inequalities", please click the Inequality ppt Inequality and Group of Inequality ppt tab.

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Update Time: 2024-06-29

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

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