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"Linear Inequalities of One Variable" PPT Courseware on Inequalities and Inequality Groups (Lesson 1)
Part One: Learning Objectives
Understand and master the concept of linear inequalities of one variable; (Key points)
Be able to use the properties of inequalities to skillfully solve linear inequalities of one variable. (Key points and difficulties)
PPT on linear inequalities of one variable, part 2: introduction of new lesson
Interesting reading
Once, Lu Ban's hand was accidentally cut by a grass leaf. He found that the edges of the grass leaves were densely covered with small teeth, so he made an association and invented a saw based on the structure of the grass.
Luban used the thinking method of "analogy" here, which is also an important method commonly used in mathematics learning.
Review introduction
1.What is a linear equation of one variable?
Contains only one unknown number, and the degree of the unknown number is 1",
An equation with integers on both sides of the equal sign is called a linear equation of one variable.
2. Basic properties of inequalities:
Property 1 of inequality: If the same number (or formula) is added (or subtracted) to both sides of the inequality, the direction of the inequality sign remains unchanged.
Property 2 of inequality: If both sides of the inequality are multiplied (or divided) by the same positive number, the direction of the inequality sign remains unchanged.
Property 3 of inequality: If both sides of the inequality are multiplied (or divided) by the same negative number, the direction of the inequality sign changes.
PPT on linear inequalities of one variable, the third part: knowledge explanation
The concept of linear inequality of one variable
Observe the following inequality:
x-7>26, 3x-7>26, -4x>3.
What characteristics do they have in common?
Each inequality contains only one unknown; and the degree of the unknown is 1.
The definition of linear inequality of one variable:
It contains only one unknown number, and the highest degree of the unknown number is 1. An inequality like this is called a linear inequality of one variable.
practice
1. Among the following expressions, which one is a linear inequality of one variable ()
A.5+4>8B.2x-1
C.2x≤5 D. 1/x-3x≥0
2. Which of the following inequalities are linear inequalities of one variable?
(1) 3x+2>x–1 (2)5x+3<0
(3) 1/x+3<5x−1 (4)x(x–1)<2x
Solving linear inequalities of one variable
Solve the inequality:
3x-1<5x+11
Solution: Move the terms and get
3x-5x<11+1
Combine similar items to get
-2x<12
The coefficient is changed to 1, and we get
x>-6
PPT on linear inequalities of one variable, part 4: training in class
1. Solve the following inequalities and express their solutions on the number line:
(1) 4x-3 < 2x+7;
Solution: (1) The solution set of the original inequality is x<5, which is expressed on the number axis as
(2) The solution set of the original inequality is x≤-11, which is expressed on the number axis as:
2. The smallest positive integer solution for a≥1 is m, and the largest positive integer solution for b≤8 is n. Find the solution set of the inequality (m+n)x>18 about x.
Solution: Because the smallest positive integer solution for a≥1 is m, so m=1.
Because the largest positive integer solution for b≤8 is n, so n=8.
PPT on linear inequalities of one variable, Part 5: Class summary
Solution set of linear inequalities of one variable
Steps to solve linear inequalities of one variable
Keywords: Free download of PPT courseware for mathematics in the second volume of the seventh grade of the People's Education Press, PPT download of linear inequalities in one variable, PPT download of inequalities and inequality groups, .PPT format;
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