"Properties of Inequalities" Inequality and Inequality Group PPT Courseware 3

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"Properties of Inequalities" Inequality and Inequality Group PPT Courseware 3

From a+2=b+2, can we get a=b?

From a-2=b-2, can we get a=b?

From 0.5a=0.5b, can we get a=b?

From -2a= -2b, can we get a=b?

Basic property of equation 1:

If the same number or formula is added (or subtracted) to both sides of the equation, the equation still holds.

If a=b, then a±c=b±c

Basic property 2 of equation:

If both sides of the equation are multiplied (or divided) by the same number that is not 0, the equation still holds

If a=b, then ac=bc or a/c=b/c (c≠0),

teaching objectives

1. Master the basic properties of inequalities.

2. Use the basic properties of inequalities to solve inequalities and convert simple linear inequalities of one variable into the forms of "xa" and "x≥a".

Today we are learning the three basic properties of inequalities

Basic properties of inequalities 1:

If a > b, then a±c > b±c. That is to say, the same number (or formula) is added (or subtracted) to both sides of the inequality, and the direction of the inequality sign remains unchanged.

Basic properties of inequalities 2:

If a > b, c > 0, then ac > bc (or a/c=b/c (c≠0)) means that both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality sign is different. Change.

Basic property of inequalities 3:

If a>b, c<0, then ac

The difference and connection between the properties of equality and the properties of inequality

Difference: When both sides of the equation are multiplied (or divided) by the same number (the divisor is not 0), the results are still equal; when both sides of the inequality are multiplied (or divided) by the same number (the divisor is not 0), the result will be There are two situations: if it is a positive number, the direction of the inequality sign does not change; if it is a negative number, the direction of the inequality sign changes, and both sides of the inequality are multiplied by 0, and the results are equal.

Connection: Both the properties of inequalities and properties of equality discuss the situation where the same number is added or subtracted from both sides and the situation when both sides are multiplied or divided by the same number (the divisor is not 0), that is, the "form" is consistent. .

Exercise: Transform the following inequalities into the form x > a or x < a

(1)x-5>-1

Solution: According to the basic property 1 of the inequality, adding 5 to both sides of the inequality gives x> 4

(2)-2x>4

Solution: According to the basic property 3 of the inequality, divide both sides of the inequality by -2, x<-2

(3)7x<6x-6

Solution: According to the basic property 1 of the inequality, subtract 6x from both sides of the inequality to get x<-6

summary:

When using the basic properties of inequalities to deform, when both sides of the inequality are multiplied (or divided) by the same letter, the key to the problem is what number the letters represent. This determines whether to use basic properties 2 or 3 of the inequality, and also It’s a matter of whether the inequality sign needs to change direction.

Keywords: Teaching courseware of inequalities and groups of inequalities, teaching courseware of the properties of inequalities, PPT courseware of the second volume of seventh-grade mathematics published by the New People's Education Press, download of the seventh-grade mathematics slide courseware, download of the PPT courseware of inequalities and groups of inequalities, download of the PPT courseware of the properties of inequalities ,.ppt format

For more information about the PPT courseware "Inequalities and Inequality Groups and Properties of Inequalities", please click on the Inequality and Inequality Groups ppt Properties of Inequalities ppt tag.

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Update Time: 2024-09-09

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