Middle School Mathematics, Unary Inequalities and Unary Inequalities Group

Assuming x pieces are the original price**, and 100 pieces are 9% off**, then 900-x pieces are 6% off**.

then the profit is. The title means 800 4x-1700 1600, i.e. 2500 4x 3300 combined with 0 x+y 1000 and x,y are positive integers. So x can take any integer from 625 to 825.

Solution: If it is necessary to sell x pieces of this commodity at the original price outside of the festival and off-season, then off-season (900-x) pieces. Rule.

1000×200×(1+10%)<200(1+25%)x+100×<1000×200×(1+20%)

220000<100x+157500<24000062500<100x<82500

625 A: 625 825 pieces of this product need to be sold at the original price outside of festivals and off-seasons.

A factory has 360kg of A raw materials and 290kg of B raw materials, and plans to use these two raw materials to produce a total of 50 pieces of AB two products, known to produce one, A product needs 9kg of A raw material, 3kg of B raw material, and 4kg of A raw material and 10kg of B raw material are required to produce a B product.

1) Set up the production of x pieces of A products. Write out the inequality group 9x+4(50-x) 360 that x should satisfy, solve x 323x+10(50-x) 290, and solve x 30(2) What are the production schemes?

32 x 30 from 1).

Integer x = 30, 31, 32

That is, there are 3 production options.

A30 pieces, B20 pieces.

A31 pieces, B19 pieces.

A32 pieces, B28 pieces.

3) If the production of a product A can make a profit of 700 yuan, and the production of a B product can make a profit of 1200 yuan, then which production plan can be used to make the total profit of the production of A and B products the largest? What is the maximum profit?

Total profit y = 700x + 1200 (50-x).

60000-500x

The smaller the x, the greater the y.

That is, the plan has the largest profit, and the maximum profit = 60,000-500 30 = 45,000 yuan.

1) If x pieces of A products are produced, then 50-x pieces of B products will be produced, and 9x+4(50-x) 360 will be obtained

3x+10(50-x)≤290

2) Solve 30 x 32

So there are three schemes, ie.

30 pieces of A products, 20 pieces of B products, 31 pieces of A products, 19 pieces of B products, 32 pieces of A products, and 18 pieces of B products.

3) The production of A product x pieces, can make a profit of 700x yuan, and the production of (50-x) B product makes a profit of 1200 (50-x) yuan, then the total profit of the production of A and B products is 700x + 1200 (50-x) = -500x + 60000

Because -500<0, when x=30, there is a maximum value of 60,000-500*30=45,000 yuan.

(1) 9x+4(50-x)<=360

3x+10(50-x)<=290

2) Solve the inequality to get 30<= x < = 32, that is, x can take 30, 31, 32, that is, there are three schemes: production of 30 pieces a, 20 pieces of b. Production of 31 pieces A, 19 pieces B. Produced 32 pieces of A, 18 pieces of B

3) Profit w = 700x + 1200 (50-x) = 60000-500x When x is equal to 30, the maximum profit is 45000 yuan.

（1）9x+(50-x)*4<=360

3x+(50-x)*10<=360

The solution yields 30<=x<=32

2) and x can be taken

3) y=700x+1200 (50-x), when x=30, y is up to 450000

（1）9x<=360；3x<=290；x<=50

2) There are three: x=30 or x=31 or x=32

3) When x=30, the profit is the largest, which is 45,000 yuan.

(1) 9x+4(50-x)≤360 ①3x+10(50-x)≤290 ②

2) Solution: 9x+200-4x 360

x≤32 3x+500-10x≤ 290

7x≥210

x 30 So, when x = 30, a = 30 b = 20

When x=31, a=31 b=19

When x=32, a=32 b=18

3) Because x is the smallest, the profit is the greatest.

Therefore, the first method is adopted: 700 * 30 + 1200 * 20 = 45,000 yuan.

Solution: (1) 9x+(50-x)4 360

3x+（50-x）10≤290

The solution yields 30<=x<=32

2) 30 x 32 from (1).

There are 3 options.

3) Let the maximum profit be w

w=700x+1200（50-x）

Simplification: w=-500x+60000

The smaller the x, the greater the w.

take x=30w=-500x+60000=45000

<=360

3x+(50-x)10<=290

Finally, 30<=x<=32

2.That's 30, 31, 32.

3.Since A is less profitable than B, of course B is more produced. So: 30a, 20b, the maximum profit is 45000

Just give a good review-

Solution: 3x+a=x-7

3x-x=-7-a

2x=-7-a

x=-(7+a)/2

Since the root is a positive number, so.

7+a)/2>0

7+a)>0

7-a>0

a<-7

The value range of a is a<-7

1, Xiao Ming is x years old this year, Xiao Li is old and returns to congratulate him x - 4 years old, Xiao Yin is x + 3 years old.

x+x-4+x+3-7*3<29

x+x-4+x+3+4*3>56

Get x<17, x>15, so x=16

2. The price of the bid is 11 yuan.

3. If you don't send 7 people, then 6 people will be counted as (1-1 2-1 4-1 7) x=7, x=56 people.

1, Xiao Ming X

Xiaoli X-4

Camouflage x+3

7 years ago, the sum of their ages was x+x-4+x+3-21< and after 294 years of Douchen, the sum of their years and years was x+x-4+x+3+12>56, resulting in 1510 <10

x is an integer, so x=11

3. If there are x students in this class, then x-1 2x-1 4x-1 7<7 is solved to x<196 3 x is an integer, so the maximum number of rows x is 65

Question 1:

Subtract 5x from both sides of the inequality at the same time, then it becomes 3x+1 -3

Further, if both sides of the inequality are -1 at the same time, it becomes 3x -4, and then both sides of the inequality are divided by 3 at the same time, which is x -4 3.

The first two steps, called shifting, are actually equivalent to changing the 5x on the right to -5x to the left, and the second step is equivalent to changing the 1 on the left to -1 and moving it to the right. The main thing about moving an item is to change the plus or minus sign.

Question 2: Parenthesis: If the parenthesis is preceded by a + sign, then the positive and negative signs remain unchanged when the parentheses are preceded, if the parentheses are preceded by a number, then after the expansion, the symbol will become reversed, so after the parentheses is 3*x+3*2-1 5-2*x+2*2*2, have you noticed? The last 2 became +2*2.

The next step is to move the item, and you can come up with the answer.

In the third question, both sides of the inequality are multiplied by 6 (the least common multiple of 2 and 3) at the same time, and then, as in the second question, parentheses, shift.

The fourth problem, the solution of an inequality, the upper one gets x -6, the next one is more troublesome, the two sides of the inequality are multiplied by 20 at the same time (20 is the least common multiple of 4 and 5, if you have not learned the least common multiple, then multiply by 4 first, and then multiply by 5, so that the understanding is also believed) to get 4 (x+2)-5 (x-1) 0

As in the second question, parentheses, move items, and you can get x 13

So the answer is -6 x 13, and this merger is written as -6, x and 13 from small to large, or vice versa

The fifth diagram is also exactly the same solution, but the second inequality lends x 2, and the third gets x 3, which is more complicated to draw a number line to explain, but, if you think like this, 2 is 3, so x 2 contains 3, so at the end of the answer, write 1 x 2

If you are an elementary school student, you should not study the fifth question, and it will be easy to do it when you have learned the number line in junior high school, or you can find the information of the number line and look at it yourself.

The sixth problem, the solution of natural numbers, means that all the x's that are satisfied are listed, and the solution is the same as the fourth problem.

。。。It's so easy, are you learning?

Go step by step, don't mess yourself up.

The first question is greater than or equal to the meaning of x y, for example, x y, x is greater than or equal to y, and vice versa.

The second big problem is a group of inequalities. Solving the first and second results and then looking at the intersection is the answer.

The third problem is to calculate the solution of this inequality on the basis of the second problem, you should know what the natural number is, and then write the result that it conforms.

Elementary school students don't need to understand these junior high school students, you will naturally understand! It's good to find out now.

-2x≥-6

x 3 makes the equation unsolvable, x < 3

To make x>a, then a 3

The intersection point with the x-axis is (-2,0), and it can be seen from the graph that the intersection point of y=3x+b and the x-axis must be to the left of (-2,0), that is, when y=0, x<-2 is -b 3<-2 b>6

3.For 5- 2y=31-5a y=(31-5a) 2 - 3 2x=31-3a x=(31-3a) 2 let x,y>0, then 31 5 a 31 3

1,5-2x -1 knows x 3, x-a 0 knows x>a, the system of equations has no solution, i.e. there is no intersection between the two regions, a 3

The intersection point with the x-axis is (-2,0), and the straight line y=3x+6 also passes this point, and the drawing shows that b>6 satisfies the topic.

3.Similar to the previous problem, find the range of the a-value of the intersection of two straight lines in the first quadrant.

31 5 a 31 3 is right.

Solution: Each vehicle is booked to carry x passengers.

From the meaning of the title:

When one more person is loaded: 9(x+1)>98 Solution: x>9 When one person is missing: 9(x-1)<90 Solution: x<11 simultaneous equation obtains: x=10

Each vehicle is booked to carry 10 passengers.

According to (4) the available raw materials in 2010 800-200 + 1200 = 1800 tons, according to (3) can produce products.

1800000 20 = 90000 bags, 90000 * 4 = 360000 hours, according to (2) know that the product can be produced in 80000-

Between 90,000 bags, because the raw materials determine the production capacity, the production capacity can only be 90,000 bags, and the labor needs to be about 360,000 2,100 = 171

Person. 1. If you purchase x sets of TVs and refrigerators, the washing machine will be (15-2x).

15-2x≤1/2x

2000x+2400x+1600（15-2x）≤32400

According to the title: Solve this group of inequalities, and get 6 x 7

x is a positive integer, x=6 or 7

Plan 1: Purchase 6 TVs, 6 refrigerators, and 3 washing machines;

Option 2: Purchase 7 TVs, 7 refrigerators, and 1 washing machine.

2) Plan 1 needs to be subsidized: (6 2100 + 6 2500 + 1 1700) 13% = 4251 (yuan);

Plan 2 requires subsidy: (7 2100 + 7 2500 + 1 1700) 13% = 4407 (yuan);

The state's fiscal revenue needs to subsidize farmers by up to 4,407 yuan.

Answer: The state's fiscal revenue needs to subsidize farmers by up to 4,407 yuan.

Solution: (1) If there are x models of A type, then the B type of Tan tremor is (50-x), which is obtained according to the topic.

The inequality of the solution is 31 x 33

x is an integer, and x can be taken as 31, 32, 33

Three combinations can be designed.

There are 31 horticultural models of A type and 19 horticultural models of B type.

There are 32 horticultural models of A type and 18 horticultural models of B species.

There are 33 horticultural models of A type and 17 horticultural models of B species

2) Method 1:

Because the cost of B modeling is higher than the cost of A modeling, the less B modeling, the lower the cost, so the scheme should be selected, the cost is the lowest, and the lowest cost is.

33 800 + 17 960 = 42720 (yuan).

Method 2: Scheme needs to be 31 800 + 19 960 = 43040 (yuan).

The cost of the scheme is 32 800 + 18 960 = 42880 (yuan).

The cost of the scheme is 33 800 + 17 960 = 42720 (yuan).

The lowest cost should be selected, and the lowest cost is 42,720 yuan

Finally, I wish you success in your studies!