"Basic Properties of Inequalities" PPT courseware

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"Basic Properties of Inequalities" PPT courseware

Review the past and learn the new

1. Observe the following two sets of formulas:

The first group: 1+2=3; a+b=b+a; S = ab; 4+x = 7.

The second group: -7 < -5; 3+4 > 1+4; 2x ≤6, a+2 ≥0; 3≠4.

The first group is ____, the second group is ____

2. Expressions expressing inequality relationships such as -7<-5; 3+4 > 1+4; 2x ≤6, a+2 ≥0; 3≠4 are called inequalities.

Determine whether the following expression is an inequality:

(1)-3<0; (2)4x+3y>0

(3) x=3; (4) X2+xy+y2

(5)x≠5; (6)X+2>y+5;

Basic property of equation 1: If the same integer is added (or subtracted) to both sides of the equation, the result is still an equation

If a=b, then a±c=b±c

Basic property of equation 2: If both sides of the equation are multiplied (or divided) by the same number that is not 0, the result is still an equation.

If a=b, then ac=bc, a÷c=b÷c (c≠0)

Explore and discover

Observation: Use "<" or ">" to fill in the blanks and look for the rules.

(1)6>4 6+2____4+2

6-2____4-2

(2) –1<3 -1+2____3+2

-1-3____3-3

Discover: When the same number is added or subtracted from both sides of an inequality, the direction of the inequality sign ________

Basic properties of inequalities 1

If the same integer is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.

If a

If a>b, then a+c>b+c, a-c>b-c.

Basic properties of inequalities 2 and 3

If both sides of the inequality are multiplied (or divided by) the same positive number, the direction of the inequality sign remains unchanged.

To multiply (or divide) both sides of an inequality by the same negative number, the direction of the inequality sign must be changed.

If a>b, and c>0, then ac>bc,

If a>b, and c<0, then ac

Inequality property 1:

If the same integer is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.

Inequality property 2:

If both sides of the inequality are multiplied (or divided) by the same positive number at the same time, the direction of the inequality sign remains unchanged.

Inequality property 3:

When both sides of an inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes.

Give it a try and see who is faster

Assume m>n, fill in the blanks with ">" or "<".

(1) m-5____ n-5

(2) m+4 ____ n+4

(3) 6m ____ 6n

(4) -3m ____ -3n

give it a try

1. Given that x>y, compare the sizes of 2-3x and 2-3y.

2. Given that m(a-3)n, find the range of a.

emerging

Example 1: It is known that x>y, try to compare the sizes of -2x and -2y, and explain the reason

Variant 1: Compare the sizes of a-2x and a-2y

Variant 2: Compare the sizes of a-2x/3 and a-2y/3

Variation 3: If x>y, and (a-3)x<(a-3)y, find the value range of a.

Variation 4: If x>y, compare the sizes of (a-3)x and (a-3)y?

Give it a try and see who is faster

(1) 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

(2) It is known that a

A.4a<4b B.-4a<-4b

C.a+4

Expand and extend

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)

Basic properties of equations and inequalities

Basic properties 1

If the same integer is added (or subtracted) to both sides of the equation, the result is still an equation

If the same integer is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.

Basic properties 2

If both sides of an equation are multiplied (or divided) by the same non-zero number, the result is still an equation.

If both sides of the inequality are multiplied (or divided) by the same positive number, the direction of the inequality sign remains unchanged;

When both sides of an inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes.

Keywords: teaching courseware on the basic properties of inequalities, Qingdao edition eighth grade mathematics volume 2 PPT courseware download, eighth grade mathematics slide courseware download, basic properties of inequalities PPT courseware download, .PPT format;

For more information about the "Basic Properties of Inequalities" PPT courseware, please click on the "Basic Properties of Inequalities" ppt tab.

"Basic Properties of Inequalities" PPT download:

"Basic Properties of Inequalities" PPT Download Part One: Learning Objectives: Know the basic properties of inequalities, and be able to use the basic properties of inequalities to transform inequalities. [Learning Focus] The derivation process of the basic properties of inequalities. [Difficulties in Learning] Utilization does not vary..

"Basic Properties of Inequalities" PPT:

"Basic Properties of Inequalities" PPT Part 1: Think about what properties equations have? Do inequalities have these similar properties? Basic property of equation 1: If the same integer is added (or subtracted) to both sides of the equation, the equation still holds. If a=b,..

"Basic Properties of Inequalities" PPT courseware 3:

"Basic Properties of Inequalities" PPT Courseware 3 Knowledge Review (1) If the same integer is added (or subtracted) to both sides of the equation, the result is still an equation. If a=b, then a+c=b+c (or a-c=b-c) (2) Both sides of the equation are multiplied by (or divided by) the same integer (divided by..

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Update Time: 2024-11-22

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