"Inequality" Inequality and Inequality Group PPT Courseware 2

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"Inequality" Inequality and Inequality Group PPT Courseware 2

question

A car traveling at a constant speed is 50 kilometers away from point A at 11:20. If it wants to pass point A before 12:00, what conditions should the vehicle speed meet?

analyze:

Assume the vehicle speed is x kilometers/hour

From a time point of view, if the car has to drive through point A before 12:00, it will take less than 2/3 hours to travel 50 kilometers at this speed, that is,

50/x＜2/3 ①

From the perspective of distance, if the car has to drive through point A before 12:00, then the distance traveled for 2/3 hours at this speed will be more than 50 kilometers, that is

2/3x>50 ②

Definition: Expressions that use "<" or ">", "≤" or "≥" to express a large or small relationship are called inequalities. Expressions that use a "≠" sign to express an unequal relationship like a+2≠a-2 are also inequalities. .

Note: “＜”, “＞”, “≠”, “≤”, and “≥” are all inequality signs

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

Substitution is a simple, practical way to test whether a value is a solution to an inequality;

think

Determine which of the following numbers are solutions to the inequality 2/3x>50:

76, 73, 79, 80, 74.9, 75, 75.1, 90, 60

Can you find other solutions to this inequality? How many solutions does this inequality have? Can you name its solution set?

Think about it:

1. Are the solutions of inequalities and the solution sets of inequalities the same?

2. Are the solutions to inequalities the same as solving inequalities?

try practice

Which of the following statements is correct ( )

A. x=3 is the solution of 2x+1>5

B. x=3 is the only solution to 2x+1>5

C. x=3 is not a solution to 2x+1>5

D. x=3 is the solution set of 2x+1>5

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

For example, the solution set of inequality 2/3x>50 can be expressed by the inequality x>75

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.

Notice

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

①Draw the number line; ②Determine the boundary points; ③Determine the direction.

2. Use the number line to represent the solution set of the inequality. Remember the following rules:

If it is greater, draw it to the right, if it is less, draw it to the left; if there is an equal sign (≥, ≤), a solid point will be drawn, if there is no equal sign (>, <), a hollow circle will be drawn.

think about it

We know that 2x+1=5 is called a linear equation of one variable, so what do you think the inequality 2x+1>5 should be named?

Similar to a linear equation of one variable, an inequality that contains an unknown number and the degree of the unknown is 1 is called a linear inequality of one variable.

Which of the following expressions are linear inequalities of one variable ( )

A. 4x-2y≤0

B. x≥-11

C. x2-1≤0

D. 50/x＜2/3

To determine whether an expression is a linear inequality of one variable, four conditions must be met:

①The formula contains only one unknown number;

②The degree of the unknown is 1;

③The expressions are connected with the inequality sign

④The denominator does not contain unknown numbers

Try the exercise: express with inequalities

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.

Solution: ⑴ a+1>0 ⑵2y+1<3 ⑶3y+2x≥0 ⑷3x+2≤5

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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: 2024-07-01

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