"Group of linear inequalities of one variable" PPT courseware

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"Group of linear inequalities of one variable" PPT courseware

Recall: 1. What is the solution set of an inequality?

All the solutions of an inequality form the set of solutions to the inequality, which is referred to as the solution set of the inequality.

2. What are the steps for solving linear inequalities of one variable?

Remove denominators, remove brackets, move terms, combine similar terms, and reduce the coefficient of the unknown number to 1.

When expressing the solution set of an inequality on a number line, you should pay attention to:

If it is greater, draw it to the right, if it is less, draw it to the left; if there is an equal sign, draw a solid dot, if there is no equal sign, draw an open circle.

Observe and think:

(1) In the Cartesian coordinate system, when x satisfies what conditions? Point P (3x-9,1+x) is in the second quadrant?

3x-9<0

1+x>0

Similar to a system of equations, two or more such inequalities are combined to form a system of inequalities.

1. The concept of a group of linear inequalities of one variable

(1) What does "one yuan" mean?

It means that the inequality group contains only one unknown number.

(2) What does "once" mean?

Refers to the degree of the unknown in the inequality being 1.

(3) Concept

From several linear inequalities of one variable containing the same unknown number

The resulting set of inequalities is called a set of linear inequalities of one variable.

2. Solution set of linear inequalities of one variable

Please find the solution sets of the two inequalities in the inequality group.

3x-9<0

1+x>0

Solving inequality ①, we get: x<3

Solving inequality ②, we get: x>-1

Concept: The common part of the solution set of all inequalities in an inequality group is called the solution set of this inequality group.

Based on the above solution process, what do you think are the general steps to solve a system of linear inequalities of one variable?

Steps to solve a system of linear inequalities of one variable:

(1) Find the solution set of each inequality in the inequality group;

(2) Use the number line to find the common parts of the solution sets of these inequalities;

(3) Based on the common parts of the solution sets of several inequalities, write the solution set of this inequality group.

(1) Concept

1. An inequality group consisting of several linear inequalities of one variable is called a group of linear inequalities of one variable.

2. The common part of the solution sets of several linear inequalities of one variable is called the solution set of the group of linear inequalities composed of them.

3. The process of finding the solution set of a set of inequalities is called solving a set of inequalities.

(2) Methods for solving simple linear inequalities of one variable:

(1) Find the solution set of each inequality in the inequality group

(2) Use the number line to find the common parts of the solution sets of these inequalities

(3) Based on the common parts of the solution sets of several inequalities, write the solution set of this inequality group.

(If the common part cannot be found, the inequality group has no solution)

Utilization rules:

If the same is bigger, choose the bigger; if the same is smaller, choose the smaller;

Look in the middle between big and small, big and small, there is no solution.

practise

1. If the inequality group -2＜x≤4, x+m＞1 has 4 integer solutions, find the value range of m? What if there is no solution?

2. If the inequality group x-a≥0,3-2x>-1 has 3 positive integer solutions, find the value range of x?

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Update Time: 2024-10-20

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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