To solve inequalities and 30 unary equations in the first year of junior high school, with answers..

Inequality exercises.

1. Multiple choice questions.

1.The owner of a shopping mall sells a commodity, and he has to be no less than 20% of the purchase price, but in order to make more profits, he marks the price at 80% higher than the purchase price. If you want to buy this kind of product with a price of 360 yuan, the maximum price reduction can be reduced by the owner of the product** (

a $80 $.

2.A hotel has two rooms, three rooms, four rooms for tourists to rent, a tour group of 20 people are ready to rent these three rooms at the same time a total of 7 rooms, if each room is full, the rental plan has (

Species of species.

2. Fill in the blanks. 3.The purchase price of apples is yuan per kilogram, and it is estimated that 5% of the apples are normally lost in sales, so in order to avoid losses, the merchants should set the selling price at least at least yuan per kilogram.

4.A shopping mall has launched a shopping gold card, with which the card can be discounted by 20% in the shopping mall, but each card purchase fee of 100 yuan will be charged when applying for a gold card, and the cumulative shopping amount according to the marked price will be x yuan, when x> time, apply for a gold card to save money.

3. Practical questions.

5.A junior high school in our city held a "8 Rong 8 Shame" knowledge competition, a total of 50 questions, the answer regulations: 3 points for 1 question, 1 point for 1 wrong answer, 0 points for not answering, Xiaojun participated in the competition, only 20 of the questions were answered, to make the final score not less than 50 points, ask Xiaojun at least to answer the question correctly?

2007 Nanchong) a store needs to buy a batch of TVs and washing machines, according to market research, it is decided that the purchase of TVs is not less than half of the purchase of washing machines The purchase price and selling price of TVs and washing machines are as follows:

Category: Television, washing machine.

Purchase price (yuan) 1800 1500

The selling price (yuan) 2000 1600

A total of 100 televisions and washing machines are planned to be purchased, and the store can raise up to $161,800

1) Can you help the store calculate how many options there are? (Excluding costs other than the purchase price).

2) Which purchase plan will make the most profit after the store sells the purchased TV and washing machine? And find the maximum profit (profit, selling price, purchase price).

6.The Fulin Garment Factory currently employs 24 garment workers who make shirts and pants of a certain brand every day, each of which can make 3 shirts or 5 pairs of pants per day.

1) If the factory requires the same number of shirts and pants to be made every day, how many people should be arranged to make shirts and pants?

2) It is known that a profit of 30 yuan can be obtained by making a shirt, and a profit of 16 yuan can be obtained by making a pair of pants, if the factory requires a profit of not less than 2100 yuan per day, how many workers need to be arranged to make shirts at least?

A1 c

2. c3 .$4.

4.> 500 yuan.

5.Answer at least 18 questions correctly.

6.(1) 15 people should be arranged to make shirts and 9 people to make pants.

2) At least 18 workers need to be arranged to make shirts.

14x＋3＜3x

x<-3

24－x>4

x<032x－4>0

x>24－ x＋2＞5

x<3

x<-3

510-3（x+6）<1

10-3x-18<1

3x<9

x>361+x/3>5-(x-2)/2

6+2x>30-3x+6

5x>30

x>67x(2x-3)<5(x-1)

4x-6<5x-5

x>-1

8(y+1)/3-(y-1)/2>(y-1)/6-2y>-6

y<392(x-1)-72

x>-8

113[x-2(x-7)]<4x

7x<-42

x>612y-(3y-8)/3<[2(10-y)]/7+121y-21y+56<60-6y+21

6y<25

y<25/6

131/2(3y-1)-1/5y-3/2

15x-1/2[x-1/2(x-1)]<2/3(x-1)12x-6x+3x-6<8x-8

x<-5

16(>(x-5)/2

24x+54-30-20x>15x-75

x<9173-(x-1)/4>2+[3(x-1)]/8-5x>1

x<-1/5

1820x<15(x+6)

5x<90

x<18

196x-2(15-x)>60

8x>90

x>207x+4(10-x)<550

3x<15

x<5 Note: This is the score line.

Absolutely original, I played for half an hour, so let's give a hard score.

You can refer to the sample questions in the textbook. The best type of question.

1.There are 60 workers in a production workshop to produce sunglasses, and 1 worker can produce 200 lenses or 50 frames per day. How should workers be assigned to produce lenses and frames to match the products produced on a daily basis?

Solution: Suppose there are x workers producing lenses and (60-x) workers producing frames every day, and a pair of glasses has one frame and 2 lenses, so the equation can be set as 200x=(60-x)*50*2

Divide both sides of the equation by 100 at the same time

2x=60-x

3x=60x=20

20 workers produce lenses and 40 workers produce frames.

2.A school student spring outing, there are 36 and 42 car cars. If you only use a 36-seater car, you can just fill the seats.

If you only use a few 42-seater cars, you can use one less, and one car is not full, but more than 30 people. It is known that 36-seater cars are 400 yuan and 42-seater cars are 440 yuan. (1) How many people are on the spring outing?

2) Design a method that saves the most money.

Solution (1): If you rent a 36-seater car to rent x cars, the number of people on the spring outing is 36x, if you rent a 42-seater car to rent (x-1) cars, there are (x-2) full cars, and the number of people on the spring outing exceeds [42 (x-2) + 30] people, less than [42 (x-1)] people; Depending on the title, groups of inequalities can be listed:

36x﹥42(x-2)+30

36x﹤42(x-1)

The solution set for the inequality group is 7 x 9

The integer solution of the inequality group is x=8

When x=8, 36x=36 8=288

A: There were 288 people on the spring outing.

2): 8 cars to rent a 36-seater car, a total of money = 8 400 = 3200 yuan.

Renting a 42-seater car costs 8-1 = 7 cars, and it costs a total of money = 7 440 = 3080 yuan.

A: The most cost-effective option is to rent 7 cars with 42 seats.

1.Each brand A computer is 6,000 yuan, and each brand B desk is 150 yuan. Sellers sell at a discount to customers who make a large purchase at one time.

Provisions: If you buy more than 35 A brand computers (including 35 units) at a time, you will be sold at a 9% discount; If you purchase more than 600 B brand desks (including 600 desks) at a time, you will be sold at a 20% discount. The school plans to spend 270,000 yuan to buy computers and desks, including no less than 35 computers and no less than 600 desks.

There are two options:

a. 35 computers + 675 desks.

b. 36 computers + 630 desks.

6000x* i.e.

5400x+120y=270000 (1) x is the number of computers, not less than 35 (2).

y is the number of desks, not less than 600 (3).

Because the unit price of the computer is 45 times the unit price of the desk.

So (1) again.

45*120x+120y=270000

When x=35, y=675

y=675-45n and y is not less than 600

So n is 0 or 1 i.e.

y is 675 or 630 and x is 35 or 36

Get two scenarios:

a. 35 computers + 675 desks.

b. 36 computers + 630 desks.