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"Group of linear inequalities of one variable" PPT courseware 2
learning target
Knowledge and skills:
1. Understand the concepts and meanings of linear inequalities of one variable and their solution sets.
2. Be able to solve linear inequalities of one variable; be able to use the number line to find the solution set of inequalities.
Process and methods:
Understand the differences and connections between linear inequalities of one variable and linear inequalities of one variable.
Emotional attitudes and values:
By exploring solutions to linear inequalities of one variable and determining solution sets, you can further experience the role of analogy thinking and the combination of numbers and shapes in solving problems.
Knowledge review:
1. The definition of linear inequality of one variable: _________.
2. The solution set of linear inequalities of one variable: _________.
Explore new knowledge
Similar to a system of equations, combining two or more linear inequalities of one variable forms a system of linear inequalities of one variable.
Notice:
(1) Each inequality must be a linear inequality of one variable;
(2) The inequality must contain only the same unknown number;
(3) The number of inequalities is at least two or more.
How to solve this set of inequalities?
2x-2≥x+1
x-2<3
Solve inequality ① to get x≥3
Solve inequality ② to get x<5
Then x can only be: 3≤x<5
Generally, the common part of the solution sets of several inequalities is called the solution set of the inequality group composed of them.
To solve a system of inequalities is to find its solution set.
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.
summary
(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.
(3) Note:
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.
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