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"Group of linear inequalities of one variable" PPT courseware 2 on inequalities and inequalities
Knowledge review:
1. Briefly describe the basic steps for solving linear inequalities of one variable.
2. Solve the following inequalities and express the solution set on the same number axis
Combining several linear inequalities with the same unknown numbers together forms a group of linear inequalities of one variable.
How to solve a system of linear inequalities of one variable
Key: Determine the solution set of the inequality group
1. After solving each inequality in the inequality group, use the number line to take out the common part of the solution of each inequality, which becomes the solution of the inequality group.
2. Use formula method:
Take the big one for the bigger one, the small one for the smaller one, look for the big and small ones in the middle, and look for the big and small ones nowhere.
Have you learned it?
1. In the plane rectangular coordinate system, point (2x-6, x-5) is in the fourth quadrant, then the value range of x is ( )
A. 3
C. -5
2. The negative integer solution of the inequality group x≥-2 x>-3 is ( )
A. -2, 0, -1 , B. -2
C. -2, -1, D. Unsure.
3. The integer solution of the inequality group 1-2x≥0 2x-1>3 is ( )
A, 0 B, -1, 1
C. 0,1 D. No solution
practise
1. A triangle is formed with line segments 3, 4, and x-5 as sides, then the value range of x is _______
Solution: According to the meaning of the question, we get X-5>1 X-5<7. The solution is 6
2. Satisfy the inequality group 3x - 6 ≤2x-4 2x + 4 >0, then there are ___ positive integer values of x
Solution: The solution set of the inequality system is -2
Then there are 4 positive integer values of x, they are -1, 0, 1, 2.
Do it
The school needs to burn a batch of CDs. If it is burned by a computer company, it will cost 8 yuan per disc. If the school burns it by itself, in addition to renting a burner for 120 yuan, each disc will also cost 2 yuan.
(1) Write the functional relationship between the cost y (yuan) and the number of burned discs x (pieces) in the two methods
(2) Ask which method is more cost-effective
Solution: (1) The cost for the school to go to the computer company to burn: y1=8x
The cost of the school’s own recording: y2=120+2x
(2) From y1>y2, we get 8x>120+2x x>20
Therefore, it is more cost-effective for the school to engrave more than 20 sheets by itself.
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For more information about the PPT courseware "Group of linear inequalities of one variable, group of inequalities and groups of inequalities", please click on the tag of "Group of linear inequalities of one variable ppt, Inequalities and Groups of Inequalities ppt".
"Group of linear inequalities of one variable" PPT courseware 3:
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"Group of linear inequalities of one variable" PPT courseware 2:
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