ta có 

           \(\frac{x+1}{212}+\frac{x+2}{211}+\frac{x+3}{210}+\frac{x+4}{209}=-4\)\(-4\)

\(\Rightarrow\left(\frac{x+1}{212}+1\right)+\left(\frac{x+2}{211}+1\right)+\left(\frac{x+3}{210}+1\right)+\left(\frac{x+4}{209}+1\right)=-4+4\)

 =>   \(\frac{x+1+212}{212}+\frac{x+2+211}{211}+\frac{x+3+210}{210}+\frac{x+4+209}{209}\) =\(0\)

=>     \(\frac{x+213}{212}+\frac{x+213}{211}+\frac{x+213}{210}+\frac{x+213}{209}\)=\(0\)

=>      (x+213) \(\left(\frac{1}{212}+\frac{1}{211}+\frac{1}{210}+\frac{1}{209}\right)\)=0

mà\(\left(\frac{1}{212}+\frac{1}{211}+\frac{1}{210}+\frac{1}{209}\right)\)\(\ne0\)

=>x+213=0   => x=-213

vậy x= -213

\(\frac{x+1}{212}+\frac{x+2}{211}+\frac{x+3}{210}+\frac{x+4}{209}=-4\)

\(\Rightarrow\frac{x+1}{212}+1+\frac{x+2}{211}+1+\frac{x+3}{210}+1+\frac{x+4}{209}+1=-4+4=0\)

\(\Rightarrow\frac{x+213}{212}+\frac{x+213}{211}+\frac{x+213}{210}+\frac{x+213}{209}=0\)

\(\Rightarrow\left(x+213\right)\left(\frac{1}{212}+\frac{1}{211}+\frac{1}{210}+\frac{1}{209}\right)=0\)

\(\Rightarrow x+213=0\Leftrightarrow x=-213\)

dễ thì dễ thiệt nhưng sao dài quá vậy

Qua chuan

\(\left(X+5\right)-\left(X-9\right)=X+2\)\(2\)

\(=>X+5-X+9=X+2\)

\(=>\left(X-X\right)+\left(5+9\right)=X+2\)

 \(=>0+14=X+2\)

\(=>14=X+2\)

\(=>X=12\)

(x+5)-(x-9)=x+2

x+5-x+9=x+2

x-x+14=x+2

12=x(cũng bớt mới về đi 2 đơn vị)

hoặc x=14-2suy ra x=12

làm cau 2 đi mk tích

\(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)

\(< =>\frac{5x-131}{19}=\frac{1631-52x-\frac{38x-684}{5}}{209}\)

\(< =>\left(5x-131\right)209=\left(1631-52x-\frac{38x-684}{5}\right)19\)

\(< =>55x-1441=1631-52x-\frac{38x-684}{5}\)

\(< =>3072-107x=\frac{38x-684}{5}\)

\(< =>\left(3072-107x\right)5=38x-684\)

\(< =>15360-535x-38x-684=0\)

\(< =>14676=573x< =>x=\frac{14676}{573}=\frac{4892}{191}\)

nghệm xấu thế 

\(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)

\(< =>\frac{8x+176}{45}-\frac{41x+817}{45}=\frac{11x+415}{45}\)

\(< =>993-33x-11x-415=0\)

\(< =>578=44x< =>x=\frac{289}{22}\)

Bài 1: 

b) Phương trình đã cho tương đương với phương trình:

\(\frac{8\left(x+22\right)-55\left(7x+149\right)-6\left(x+12\right)}{45}=\frac{9\left(x+35\right)+2\left(x+50\right)}{45}\)

\(\Leftrightarrow44x=-1056\)

\(\Leftrightarrow x=-24\)

Vậy x=-24 là nghiệm của phương trình

c) Phương trình đã cho tương đương với phương trình:

\(\frac{3x+6}{70}-\frac{x+4}{24}=\frac{32x+19}{60}+\frac{2}{3}\)

\(\Leftrightarrow12\left(3x+6\right)-35\left(x+4\right)=14\left(32x+19\right)+560\)

\(\Leftrightarrow-447x=894\)

\(\Leftrightarrow x=-2\)

Vậy x=-2 là nghiệm của phương trình

Có 1/3+3/35=44/105

Có 4/7+3/5+1/3=158/105

=> 44/105< x/210<158/105         MC: 210

=> 88/210< x/210< 316/210

Vậy x thuộc {89;90;91;92;...;315}

Ta có : 

\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

\(\Leftrightarrow\)\(\frac{70}{210}+\frac{18}{210}< \frac{x}{210}< \frac{120}{210}+\frac{126}{210}+\frac{70}{210}\)

\(\Leftrightarrow\)\(\frac{70+18}{210}< \frac{x}{210}< \frac{120+126+70}{210}\)

\(\Leftrightarrow\)\(\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)

\(\Leftrightarrow\)\(88< x< 316\)

\(\Rightarrow\)\(x\in\left\{89;90;91;...;314;315\right\}\)

Vậy \(x\in\left\{89;90;91;...;314;315\right\}\)

Chúc bạn học tốt ~ 

#)Giải :

1. 

Ta có : \(\frac{n+1}{n+2}>\frac{n}{n+2}>\frac{n}{n+3}\)

\(\Rightarrow\frac{n+1}{n+2}>\frac{n}{n+3}\)

2. 

a) \(x\left(104,5-14,1+9,6\right)=25\)

\(x\times100=25\)

\(x=25\div100\)

\(x=0,25\)

Bài 1 : Ta có :\(\frac{n+1}{n+2}>\frac{n}{n+2}>\frac{n}{n+3}\)

\(\Leftrightarrow\frac{n+1}{n+2}>\frac{n}{n+3}\)

Bài 2 : \(104,5\cdot x-14,1\cdot x+9,6\cdot x=25\)

\(\Leftrightarrow\left[104,5-14,1+9,6\right]\cdot x=25\)

\(\Leftrightarrow100\cdot x=25\)

\(\Leftrightarrow x=\frac{1}{4}\)

\(1+2+3+4+...+x=210\)

Số số hạng của dãy là : \((x-1):1+1=x\) số

Cho nên tổng của dãy đó là : \(\frac{x(x+1)}{2}=210\)

\(\Leftrightarrow x(x+1)=420\)

\(\Leftrightarrow x(x+1)=20\cdot21\)

\(\Leftrightarrow x=20\)

\(x-\frac{3}{4}=1-\frac{5}{6}\)

\(\Leftrightarrow x-\frac{3}{4}=\frac{1}{6}\)

\(\Leftrightarrow x=\frac{1}{6}+\frac{3}{4}=\frac{11}{12}\)