The eighth chapter is the comprehensive test of one-dimensional linear inequality in seventh grade mathematics. 1. multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * *).
1. If m>n and the following inequality are not necessarily correct, it is ().
A.m+2 & gt； n+2b . 2m & gt； 2n C. D. m2 > nitrogen.
2. Solve inequality 2x? X- 1, whose solution set is correct on the number axis ().
A B C D
3. If the solution set of a linear inequality group about X is represented on the number axis as shown in figure 1, then the solution of this inequality group
The set is ()
A.-2
Figure 1
4. Let the inequality x- 1? 2 and 3x-7
A.3, 4 B. 4, 5 C. 3, 4, 5 D. does not exist.
5. If |x-2|=x-2, then the value range of x is ().
A.x？ 2 B. x？ 2 C. x & lt2d . x & gt； 2
6. The number of integer solutions of inequality group is ()
countless/innumerable
7. If a is an integer, compare the sizes of a and 3a, and the following statement is true ().
A.a & gt3a B. a & lt3a C. a=3a D. Not sure.
8. The purchase price of a commodity is 120 yuan, and the profit that a merchant can get from selling such a commodity is 20% of the purchase price ~
30%, the price range is ()
A. 144 ~ 156 yuan B. 126 ~ 144 yuan C. 136 ~ 154 yuan D.145 ~1.
9. If the solution set of the inequality group about x is x >；; 1, then the value range of a is ()
A.a & gt 1 b . a & lt； 1 C. a？ 1 D. a？ 1
10. The charging standard for taxis in Dongying City is: the starting price is 8 yuan (that is, you have to pay 8 yuan fare if the driving distance is less than 3km). After 3km, for every increase of 1km, 1.5 yuan will be charged (if it is less than 1km, it will be counted as 1km).
The driving distance is X kilometers, and the taxi fare is 15.5 yuan, so the maximum value of X is ().
A. 1 1
Fill in the blanks (this topic is entitled ***8 small questions, with 4 points for each small question and 32 points for * * *).
1 1. 3x and 9 are nonnegative and are represented by inequalities.
12. If a>b, then ac2 bc2.
13. If X? The minimum value of 2 is a, x? The maximum value of -6 is b, so a+b = _ _ _ _ _ _.
14. Write the solution set as a linear inequality of x> 1.
15. If the point (1-2m, m-4) is in the third quadrant, the range of m is.
16. when a _ _ _ _ _ _ the solution set of inequality is X >；; 2.
17. If the inequality group has no solution, the range of a is _ _ _ _ _ _.
18. At present, 46 tons of relief materials are transported to the disaster-stricken areas by two transport vehicles, A and B. Each car of A weighs 5 tons, and each car of B weighs 4 tons. If the number of vehicles does not exceed 10, at least one A vehicle needs to be arranged.
Third, answer the question (this big question is ***5 small questions, ***58 points)
19.( 10 points) Three known linear inequalities: 2x>4, 2 times? x- 1，x-3 & lt； Please choose what you like.
Huan's two inequalities form an inequality group. Find the solution set of this inequality group, and the solution set is shown on the number axis of Figure 2.
(1) Your inequality set is:
(2) Solution:
20.( 10) If the value of the formula is not less than the value of the formula, find the value range of x. 。
2 1.( 12 points) An electrical appliance store sells two models of calculators, A and B, and the purchase price of the two calculators is divided.
Don't sell five A-type calculators and 1 B-type calculators in every shopping mall in 40 yuan, 30 yuan, and 76 yuan will make a profit; Selling 6 A-type calculators and 3 B-type calculators can make a profit 120 yuan.
(1) Find the sales prices of two types of calculators, A and B, respectively.
(2) The mall is going to buy 70 A-type and B-type calculators with a price not exceeding 2,500 yuan, and at least need to buy A-type for calculation.
How many pieces of equipment?
22.( 12 points) If |x-3|+(3x-y-m)2=0, when y? 0, find the range of m.
23.( 14) Two shopping malls, A and B, have the same goods and the same price, and each has different products.
Preferential scheme: after the accumulated shopping in Mall A exceeds 100 yuan, the part exceeding 100 yuan will be charged at 90%; After the accumulated shopping in Mall B exceeds 50 yuan, the part exceeding 50 yuan will be charged at 95%. Let Xiaohong spend X yuan in the same shopping mall, of which x> 100.
(1) Fill in the following table according to the meaning of the question (unit: yuan):
Accumulated shopping
The actual cost is 130 290? x
In a shopping mall 127?
At mall b, 126?
(2) What is the value of X, and the amount that Xiaohong spends in two shopping malls is the same?
(3) When Xiaohong's accumulated shopping in the same mall exceeds 100 yuan, which mall actually spends less?
Additional questions (15, not included in the total score)
Read the following materials and answer the questions.
Inequalities with unknowns in the denominator are called fractional inequalities, such as. So how do you find their solution sets?
According to the division rule of rational numbers we have learned, when two numbers are divided, the same sign is positive and the different sign is negative, which can be expressed as: ① If a >；; 0, b>0, then > 0; > 0 if a<0, b<0; 2 if a>0, b< then, 0
On the contrary: (1) if >; So, 0
If < 0, then _ _ _ _ _ or _ _ _ _ _.
(2) According to the above laws, find the solution set of inequality.
In the seventh grade, the eighth chapter of mathematics is a comprehensive examination question of one-dimensional linear inequality, and the answers are 1,1.d2.b3.c4.a5.b6.b7.d8.a9.d.
10.b Hint: According to the meaning of the question, the inequality 8+ 1.5(x-3) can be listed. 15.5.
Second, 1 1.3x-9? 0 12.？ 13.-4 14. The answer is not unique, such as 3x>3 15. 12.
16.=6 17. A? 1
18.6 prompt: if the primary transport vehicle * * * transports x tons, the secondary transport vehicle * * * transports (46-x) tons. According to the meaning of the question, what is the score? 10.
Third, 19. Solution: The answer is not unique, such as (1)
(2) x >； is obtained by solving the inequality group ①; 2.
Solve the inequality group ② and get x? - 1.
Therefore, the solution set of the inequality group is x>2, and the abbreviation is expressed on the number axis.
20. Solution: According to the meaning of the problem, can it be obtained? .
Divide by the denominator to get 3(x+9)+6? 2(x+ 1)-6。
Without brackets, 3x+27+6? 2x+2-6。
Move projects, merge similar projects, and get X? -37.
2 1. Solution: (1) Assume that the sales prices of type A and type B calculators are X yuan and Y yuan respectively.
According to the meaning of the problem, you can get a solution
A: The sales prices of A and B calculators sold in shopping malls are 42 yuan and 56 yuan respectively.
(2) Establish a type A calculator.
According to the meaning of the question, get 30a+40(70-a)? 2500, get an a? 30.
A: At least 30 Type A calculators need to be purchased.
22. solution: x-3=0, 3x-y-m=0.
The solution is x=3 and y = 9-m.
Shit, y 0，9-m？ 0, so m? 9 .
That is, the range of m is m? 9.
23. Solution: (1) Fill in: 27 1, 0.9x+10,278, 0.95x+2.5.
(2) According to the meaning of the question, it is 0.9x+ 10=0.95x+2.5, and the solution is x= 150.
So when x= 150, Xiaohong spends the same amount in two shopping malls.
(3) 0.9x+ 10 < 0.95x+2.5, and x >；; 150;
From 0.9x+ 10 >: 0.95x+2.5, x
Therefore, when Xiaohong's accumulated shopping exceeds 1 50 yuan, the actual spending in Mall A is less; When Xiaohong's accumulated shopping exceeds 100 yuan, but does not exceed 150 yuan, she actually spends less in shopping mall B.
Other issues
Solution: (1)
(2) According to the above law, the inequality is converted into or.
Get x>2 or x