Solving inequality requires detailed process (preferably with explanation) If you sell a commodity in the market, you can sell it for 200 yuan per day, and you can get a profit of 60 yuan per piece. If you reduce the price of the commodity by 20 yuan per day, you can sell 100 more pieces per day?

Solving inequality requires detailed process (preferably with explanation) If you sell a commodity in the market, you can sell it for 200 yuan per day, and you can get a profit of 60 yuan per piece. If you reduce the price of the commodity by 20 yuan per day, you can sell 100 more pieces per day?

Set a price reduction of 20x yuan
After the price reduction, the quantity will be increased by 100x per day
（200+100X)×(60-20X)
=12000-4000X+6000X-2000X²
=12000+2000X-2000X²
=2000（6+X-X²)
=2000[25/4-(1/4-X+X²)]
=2000[25/4-(X-1/2)²]
If the profit is the largest, then (x-1 / 2) 2 must be the minimum and the minimum = 0, and then x = 1 / 2
So the price reduction is 20 × 1 / 2 = 10 yuan, and the maximum profit is 2000 × 25 / 4 = 12500 yuan

The proof of inequality needs detailed process online Let the real number x, y satisfy y + x 2 = 0,0

It is proved that if y + X? = 0, then y = - x ^ 2A ^ x + A ^ y = a ^ x + A ^ (- x?) > = 2 [a ^ (x? - x)] ^ 1 / 2, because x? - x = (x-1 / 2) 2? - 1 / 4 > = 1 / 4, a ^ x + A ^ y = a ^ x + A ^ (- x ^) > = 2 [a ^ (x? - x)] ^ 1 / 2 > = 2A ^ 1 / 8, logarithm is taken on both sides because 0

I want 50 inequalities. I want to solve the process of writing inequalities in detail

1、 5 (x + 1) < x-3,
2x+21≤6-3x;
The results are as follows:
5x+5＜x-3,
2x+21≤6-3x;
∴4x＜-8,①
5x≤-15;②
According to the results of (1)
x＜-2
From (2) we can get the following results
x≤-3
The solution set of the original inequality system is as follows:
x≤-3
2、 5-7x ≥ 2X-4,
1-3/4(x-1)＜0.5;
The results are as follows:
-9x≥-9,①
-3/4x＜-5/4;②
According to the results of (1)
x≤1
From (2)
x＞5/3
The original inequality system has no solution
3、 3 (X-2) ≤ x + 2,
(1+2x)/3＞1；
The results are as follows:
3x-6≤x+2,①
1+2x＞3;②
From (1)
2x≤8
∴x≤4
From (2)
2x＞2
∴x＞1
The solution set of the original inequality system is as follows:
1＜x≤4
4、 3 (1-x) < 2 (x + 9),
(x-3)/0.5-(x+4)/0.2≤-14;
The results are as follows:
3-3x＜2x+18,①
-30x≤246;②
From (1)
-5x＜15
∴x＞-3
From (2)
x≥-4
The solution set of the original inequality system is as follows:
x＞-3
5、 2X + 3 < 9, ①
-3/2x-1≤2.②
Obtained from
2x＜6
∴x＜3
From (2)
-3x-2≤4
∴-3x≤6
∴x≥-2
The solution set of the original inequality system is as follows:
-2≤x＜3
I have tried my best to find the rest in the exercise book

(1) X-1 / 3 (x-1) ≥ 1 (2) {5x-2 > 3 (x + 1) 1 / 2 X-1 ≤ 7-3 / 2 x

① The shift term is 5x -- 4x > - 13-15, that is x > - 28 ② (whether 2x-1 and 3x-4 are molecules) are multiplied by 6 to get 4x-2 ≤ 3x-4. The shift term 4x-3x ≤ - 4 + 2, that is, X ≤ - 2 (③ and ④ are equations). ③ X-5 ＞ 1 + 2x shift leads to - 5-1 > 2x-x, that is, x < - 63x + 2 < 4x. In conclusion, X has no real number solution

I want 20 inequalities. I want to solve the process of writing inequalities in detail Don't copy the answers written by others!

System of inequalities
1、2X+3＞0
-3X+5＞0
2、2X＜-1
X+2＞0
3、5X+6＜3X
8-7X＞4-5X
4、2（1+X）＞3（X-7）
4（2X-3）＞5（X+2）
5、2X＜4
X+3＞0
6、1-X＞0
X+2＜0
7、5+2X＞3
X+2＜8
8、2X+4＜0
1/2（X+8）-2＞0
9、5X-2≥3（X+1）
1/2X+1＞3/2X-3
10、1+1/2X＞2
2（X-3）≤4
3×60 -1
4x6
2xo.1
-3x-1
4x>-12
3(2x+5)>2(4x+3)
10_ 4(x-4)x-5/4
2x+526
3x50
23.7x+4y=67
2x+8y=26
24.5x+4y=52
7x+6y=74
25.7x+y=9
4x+6y=16
26.6x+6y=48
6x+3y=42
27.8x+2y=16
7x+y=11
28.4x+9y=77
8x+6y=94
29.6x+8y=68
7x+6y=66
30.2x+2y=22
7x+2y=47
23.7x+4y=67
1.2x+9y=81
3x+y=34
2.9x+4y=35
8x+3y=30
3.7x+2y=52
7x+4y=62
4.4x+6y=54
9x+2y=87
5.2x+y=7
2x+5y=19
6.x+2y=21
3x+5y=56
7.5x+7y=52
5x+2y=22
8.5x+5y=65
7x+7y=203
9.8x+4y=56
x+4y=21
10.5x+7y=41
5x+8y=44
11.7x+5y=54
3x+4y=38
12.x+8y=15
4x+y=29
13.3x+6y=24
9x+5y=46
14.9x+2y=62
4x+3y=36
15.9x+4y=46
7x+4y=42
16.9x+7y=135
4x+y=41
17.3x+8y=51
x+6y=27
18.9x+3y=99
4x+7y=95
19.9x+2y=38
3x+6y=18
20.5x+5y=45
7x+9y=69
21.8x+2y=28
7x+8y=62
22.x+6y=14
3x+3y=27
23.7x+4y=67
2x+8y=26
24.5x+4y=52
7x+6y=74
25.7x+y=9
4x+6y=16
26.6x+6y=48
6x+3y=42
27.8x+2y=16
7x+y=11
28.4x+9y=77
8x+6y=94
29.6x+8y=68
7x+6y=66
30.2x+2y=22
7x+2y=47
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What are the steps to solve the inequality system

How many variables? If it's binary, first remove one of the unknowns and find the other, and then substitute it into the original equation to find the unknown number
If it is three variables, first eliminate an unknown number, and then become a binary system of first-order equations, and then use the method of two variables to find the two unknowns, and then replace the original equation to find the first eliminated one

Solve the following inequality system (main process) （1）X-1＜3 （2）X-1＞3 （3）X-1＞3 （4)X-1＞3 X+1＜3 X+1＞3 X+1＞3 X+1＜3 （5）2X-1＞0 （6） -3X-1＞3 （7）3（X-1）+13＞5X-2（5-X) X+1＜3 2x+1＞3 5-(2X+1)＜3-6X （8）X-3（X-2)≥4 （9）X-3（X-2)≥4 （10）2/1（X+4）＜2 3/1+2X ＞x-1 5/2X-1 ＞2/X+1 2/X+2＞3/X+3

(1) 1 + 2 = 2x ＜ 6 x ＜ 3 (2) 1 + 2 = 2x ＞ 6 x ＞ 3 (3) is the same as the second question (4) no solution (5) 1 gets x ＞ 0.52, X ＜ 2 is 0.5 ＜ x ＜ 2 (6) 1 gets x ＞ - 4 / 32, X ＞ 1 solution set is x ＞ 1 (7) 1, X ＜ 52 is x ＜ - 1 / 4 solution set is X

A symbol in differential approximate operation Higher Education Press f(xo+δx)-f(x0)=df(x)+o(δx) Is the meaning of the penultimate letter like o an absolute error sign? It's not I know the capital Delta. It's the third letter from the bottom. It's the one outside the brackets.

O (δ x) is an error function. Although it is said that the infinitesimal δ x is very small, very small, but f (XO + δ x) - f (x0) = DF (x) is not equal -- one function of the error caused by this approximation between two infinitesimal elements. O is equivalent to another F···

1 / √ 99.9)

y=1/√x=x^(-1/2)
dy=-(1/2)x^(-3/2)dx
When x = 100, DX = - 0.1,
dy=(-1/2)100^(-3/2)(-0.1)=0.05*10^(-3)=0.00005
So 1 / √ 99.9 = y + dy = 0.1 + 0.00005 = 0.10005

0

Let f (x) = LNX
f(1.1)=f(1)+0.1f'(1)=0+0.1=0.1