\(\frac{x-1}{3}+\frac{3x-5}{2}+\frac{2x}{9}+\frac{-5x+3}{9}=\frac{210}{420}\)

\(\Leftrightarrow\frac{x-1}{3}+\frac{3x-5}{2}+\frac{-3x+3}{9}=\frac{1}{2}\)

\(\Leftrightarrow\frac{6\left(x-1\right)}{18}+\frac{9\left(3x-5\right)}{18}+\frac{2\left(-3x+3\right)}{18}=\frac{9}{18}\)

\(\Rightarrow6x-6+27x-45-6x+6=9\)

\(\Leftrightarrow6x+27x-6x=9+6+45-6\)

\(\Leftrightarrow27x=54\)

\(\Rightarrow x=2\)

cái này sai đề bài

x.(x + 1) = 420

=> x.(x + 1) = 20 . 21

=> x = 20

 ( x + 1 ) = 420 : x 

 2x+x=420

3x=420

x=420:3

x=140

Đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\cdots+\frac{1}{19\cdot21}\)

\(=\frac12\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\cdots+\frac{2}{19\cdot21}\right)\)

\(=\frac12\left(1-\frac13+\frac13-\frac15+\cdots+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac12\left(1-\frac{1}{21}\right)=\frac12\cdot\frac{20}{21}=\frac{10}{21}\)

Ta có: \(\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\cdots+\frac{1}{19\cdot21}\right)\cdot420-\frac{\left\lbrack0,4\left(7,5-2,5x\right)\right\rbrack}{0,25}=212\)

=>\(420\cdot\frac{10}{21}-\frac{3-x}{0,25}=212\)

=>200-4(3-x)=212

=>200+4(x-3)=212

=>4(x-3)=12

=>x-3=3

=>x=6

a: \(C=3-3^2+3^3-3^4+\cdots+3^{23}-3^{24}\)

\(=\left(3-3^2+3^3-3^4\right)+\left(3^5-3^6+3^7-3^8\right)+\cdots+\left(3^{21}-3^{22}+3^{23}-3^{24}\right)\)

\(=\left(3-3^2+3^3-3^4\right)+3^4\left(3-3^2+3^3-3^4\right)+\cdots+3^{20}\left(3-3^2+3^3-3^4\right)\)

\(=-60\left(1+3^4+\cdots+3^{20}\right)\) ⋮60

\(C=3-3^2+3^3-3^4+\cdots+3^{23}-3^{24}\)

\(=\left(3-3^2+3^3\right)-\left(3^4-3^5+3^6\right)+\cdots-\left(3^{22}-3^{23}+3^{24}\right)\)

\(=\left(3-3^2+3^3\right)-3^3\left(3-3^2+3^3\right)+\cdots-3^{21}\left(3-3^2+3^3\right)\)

\(=21\left(1-3^3+\cdots-3^{21}\right)\) ⋮21

=>C⋮7

mà C⋮60

và ƯCLN(60;7)=1

nên C⋮60*7

=>C⋮420

b:

ĐKXĐ: y>=1

\(\left(x+1\right)^{2022}\ge0\forall x;\left(\sqrt{y-1}\right)^{2023}\ge0\forall y\) thỏa mãn ĐKXĐ

=>\(\left(x+1\right)^{2022}+\left(\sqrt{y-1}\right)^{2023}\ge0\forall x,y\)

Dấu '=' xảy ra khi x+1=0 và y-1=0

=>x=-1 và y=1

a, 2/3 của -420 là :

-420 x 2/3 = -280

Số cần tìm là :

-280 x 5/8 = -175

Vậy số cần tìm là -175

b, 1/1.3 + 1/3.5 + 1/5.7 + ... + 1/x ( x + 2 ) = 1005 / 2011

1/2 x ( 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/ ( x ( x + 2 ) = 1005 / 2011

1/2 x ( 1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/ x + 2 ) = 1005 / 2011

1/2 x ( 1 - 1/ x + 2 ) = 1005 / 2011

1 - 1 / x + 2 = 1005 / 2011 : 1/2 

1 - 1 / x + 2 = 2010 / 2011

x + 2 / x + 2 - 1 / x + 2 = 2010 / 2011

x + 2 - 1 / x + 2 = 2010 / 2011

x + 1 / x + 2 = 2010 / 2011

+> x + 1 = 2010 

x = 2010 - 1 

x = 2009

+> x + 2 = 2011 

x = 2011 - 2 

x = 2009 

Vậy x = 2009 

Tk nha Đúng đó !!

1) 2x - 378 = 122

=> 2x = 122 + 378

=> 2x = 500

=> x = 500 : 2

=> x = 250

2) 8x - 4x = 1208

=> 4x = 1208

=> x = 1208 : 4

=> x = 302

3) x - 382 = 159 : 3

=> x - 382 = 53

=>  x = 53 + 382

=> x = 435

4) 3x + 30 = 420

=> 3x = 420 - 30

=> 3x = 390

=> x = 390 : 3

=> x = 130

5) 12x  - 13x - 500 = 1500

=> -x = 1500 + 500

=> -x = 2000

=> x = -2000

1,\(2x-378=122\)

\(2x=122+378\)

\(2x=500\)

\(x=500:2\)

\(x=250\)

2,\(8x-4x=1208\)

\(x.\left(8-4\right)=1208\)

\(x.4=1208\)

\(x=1208:4\)

\(x=302\)

3,\(x-382=159:3\)

\(x-382=53\)

\(x=52+382\)

\(x=434\)

4,\(3x+30=420\)

\(3x=420-30\)

\(3x=390\)

\(x=390:3\)

\(x=130\)

5,\(12x-13x-500=1500\)

như câu 2 

\(1,2x-378=122\)\(\Rightarrow2x=500\Rightarrow x=250\)

\(2,8x-4x=1208\)\(\Rightarrow4x=1208\Rightarrow x=302\)

\(3,x-382=159\div3\)\(\Rightarrow x-382=53\Rightarrow x=435\)

\(4,3x+30=402\)\(\Rightarrow3x=372\Rightarrow x=124\)

\(5,12x-13x-500=1500\)\(\Rightarrow-x-500=1500\Rightarrow-x=1000\Leftrightarrow x=-1000\)

\(\text{a)}350:\left[19-\left(7x-3\right)\right]=350\)

\(\Rightarrow19-\left(7x-3\right)=1\)

\(\Rightarrow19-7x+3=1\)

\(\Rightarrow-7x=-21\)

\(\Rightarrow x=3\)

\(\text{b)}7.\left[109-\left(x-9\right)\right]-420=0\)

\(\Rightarrow7\left(109-x+9\right)=420\)

\(\Rightarrow118-x=60\)

\(\Rightarrow x=58\)

\(\text{c)}252-2\left\{200-4\left[90-7.\left(19-9\right)\right]\right\}.x=4\)

\(\Rightarrow2\left\{200-4\left[90-7.10\right]\right\}.x=250\)

\(\Rightarrow\left[200-4\left(90-70\right)\right].x=125\)

\(\Rightarrow\left[200-4.20\right].x=125\)

\(\Rightarrow120x=125\)

\(\Rightarrow x=\frac{125}{120}=\frac{25}{24}\)

\(\text{Xin điểm ạ}\)

350:[19-(7x-3)]=350

[19-(7x-3)]=350:350

[19-(7x-3)]=1

(7x-3)=19-1

(7x-3)=18

7x=18+3

7x=21

x=21:7

x=3

vậy x=3

7.[109-(x-19)]-420=0

7.[109-(x-19)]=0+420

7.[109-(x-19)]=420

[109-(x-19)]=420:7

[109-(x-19)]=60

(x-19)=109-60

(x-19)=49

x=49+19

x=58

vậy x=58

254-2{200-4.[90-7.(19-9)]}.x=4

254-2{200-4.[90-7.10]}.x=4

254-2{200-4.[90-70]}.x=4

254-2{200-4.20}.x=4

254-2{200-80}.x=4

254-2.120.x=4

254-240.x=4

240.x=254-4

240.x=250

x=250:240

x=25/24

vậy x=25/24