a) |5/3 - x| - |-5/6| = |-5/9|

=> |5/3 - x| - 5/6 = 5/9

=> |5/3 - x| = 5/9 + 5/6

=> |5/3 - x| = 25/18

=> \(\orbr{\begin{cases}\frac{5}{3}-x=\frac{25}{18}\\\frac{5}{3}-x=-\frac{25}{18}\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{5}{18}\\x=\frac{55}{18}\end{cases}}\)

a, \(\left|\frac{5}{3}-x\right|-\left|-\frac{5}{6}\right|=\left|-\frac{5}{9}\right|\)

\(\Leftrightarrow\left|\frac{5}{3}-x\right|-\frac{5}{6}=\frac{5}{9}\Rightarrow\left|\frac{5}{3}-x\right|=\frac{5}{9}+\frac{5}{6}=\frac{25}{18}\)

\(\Rightarrow\orbr{\begin{cases}\frac{5}{3}-x=\frac{25}{18}\\\frac{5}{3}-x=-\frac{25}{18}\end{cases}\Rightarrow}x.\)

b, \(\left|x+\frac{1}{102}\right|+\left|x+\frac{2}{102}\right|+...+\left|x+\frac{100}{102}\right|\ge0\)

\(\Rightarrow102x\ge0\Leftrightarrow x\ge0\)=> Ta có thể phá dấu GTTĐ

\(\Rightarrow x+\frac{1}{102}+x+\frac{2}{102}+...+x+\frac{100}{102}=102x\)

\(\Rightarrow100x+\frac{1+2+3+...+100}{102}=102x\Rightarrow2x\Rightarrow x.\)

5(x+3)=225-102

x+3=123/5

x=123/5-3

x=108/5

Thank

225-5(x+3)=102

=>225-5x-15=102

=>210-5x=102

=>5x=108

=>x=\(\frac{108}{5}\)

(26-3x):5=106-102=4

26-3x=4.5=20

3x=26-20=6

x=6:3

x=2

\(102+\left(26-3.x\right):5=106\)

\(\left(26-3x\right):5=106-102=4\)

\(26-3x=4.5=20\)

\(3x=26-20=6\)

\(x=6:3=2\)

`y+7/2xxy+yxx3/5=102`

`y+7/2xxyxx1xx+yxx3/5=102`

`yxx(7/2+1+3/5)=102`

`yxx5,1=102`

`y=102:5,1`

`y=20`

Vậy..

`@An`

\(a,\frac{x+1}{65}+\frac{x+2}{64}=\frac{x+3}{63}+\frac{x+4}{62}\)

\(\Rightarrow\left[\frac{x+1}{65}+1\right]+\left[\frac{x+2}{64}+1\right]=\left[\frac{x+3}{63}+1\right]+\left[\frac{x+4}{62}+1\right]\)

\(\Rightarrow\frac{x+1+65}{65}+\frac{x+2+64}{64}=\frac{x+3+63}{63}+\frac{x+4+62}{62}\)

\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}\)

\(\Rightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}=0\)

\(\Rightarrow\left[x+66\right]\left[\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\right]=0\)

Mà \(\frac{1}{65}+\frac{1}{64}-\frac{1}{63}+\frac{1}{62}\ne0\)

\(\Rightarrow x+66=0\)

\(\Rightarrow x=0-66=-66\)

Auto làm nốt câu b

a,  Cộng cả 2 vế với 2 

Ta có \(\frac{x+1}{64}+\frac{x+2}{63}+2=\frac{x+3}{62}+\frac{x+4}{61}+2\)

\(\left(\frac{x+1}{64}+\frac{64}{64}\right)+\left(\frac{x+2}{63}+\frac{63}{63}\right)=\left(\frac{x+3}{62}+\frac{62}{62}\right)+\left(\frac{x+4}{61}+\frac{61}{61}\right)\)

=>  \(\frac{x+65}{64}+\frac{x+65}{63}=\frac{x+65}{62}+\frac{x+65}{61}\)\(\)

=> \(\frac{x+65}{64}+\frac{x+65}{63}-\frac{x+65}{62}-\frac{x+65}{61}=0\)

=> \(\left(x+65\right)\left(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\right)=0\)

Do \(\frac{1}{64}+\frac{1}{63}-\frac{1}{62}-\frac{1}{61}\ne0\)=> \(x+65=0\)

=> \(x=-65\)

b ,  Lm tương tự như Câu a

Chúc bn hok tốt

a) \(\frac{x+1}{65}+\frac{x+2}{64}=\frac{x+3}{63}+\frac{x+4}{62}\)

\(\Leftrightarrow\frac{x+1}{65}+\frac{x+2}{64}+2=\frac{x+3}{63}+\frac{x+4}{62}+2\)

\(\Leftrightarrow\left(\frac{x+1}{65}+1\right)+\left(\frac{x+2}{64}+1\right)=\left(\frac{x+3}{63}+1\right)+\left(\frac{x+4}{62}+1\right)\)

\(\Leftrightarrow\frac{x+1+65}{65}+\frac{x+2+64}{64}=\frac{x+3+63}{63}+\frac{x+4+62}{62}\)

\(\Leftrightarrow\frac{x+66}{65}+\frac{x+66}{64}=\frac{x+66}{63}+\frac{x+66}{62}\)

\(\Leftrightarrow\frac{x+66}{65}+\frac{x+66}{64}-\frac{x+66}{63}-\frac{x+66}{62}=0\)

\(\Leftrightarrow\left(x+66\right)\left(\frac{1}{65}+\frac{1}{64}-\frac{1}{63}-\frac{1}{62}\right)=0\)

\(\Leftrightarrow x+66=0\)

\(\Leftrightarrow x=-66\)

CÂu b) làm tương tự:

- Trừ 3 cho hai vế ( câu a) mk cộng 2 cho hai vế)

- Tách -3 = -1-1-1 rồi kết hợp với mỗi hạng tử

CỐ LÊN NHÉ

NẾU bạn KHÔNG HIỂU thì câu b) mik sẽ làm kĩ càng và rõ ràng hơn cho bạn hiểu

=>\(\dfrac{x-5}{100}-1+\dfrac{x-4}{101}-1+\dfrac{x-3}{102}-1=\dfrac{x-100}{5}-1+\dfrac{x-101}{4}-1+\dfrac{x-102}{3}-1\)

=>x-105=0

=>x=105

- 12 . ( x - 5 ) + 7 . ( 3 - x ) = 5

=> - 12x - 12 . 5 + 7 . 3 - 7x = 5

=> - 12x - 60 + 21 - 7x = 5

=> ( - 12 - 7 )x + ( 60 + 21 ) = 5

=> - 19x + 81 = 5

=> - 19x = - 76

=> x = 4

30 . ( x + 2 ) - 6 . ( x + 5 ) - 24x = 100

=> 30x + 30 . 2 - 6x + 6 . 5 - 24x = 100

=> 30x + 60 - 6x + 30 - 24x = 100

=> 0 . x = 100

=> Không có giá trị x

( x + 1 ) + ( x + 2 ) + . . . + ( x + 99 ) = 0

=> x . 99 + ( 1 + 2 + . . . + 99 ) = 0

=> x . 99 + 4950 = 0

=> x . 99 = - 4950

=> x = - 50

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=0\)

\(x+1+x+2+...+x+99=0\)

\(99x+\left(1+2+3+...+98+99\right)=0\)

 \(99x+\frac{\left(99+1\right).99}{2}=0\)

\(99x+4950=0\)

\(99x=-4950\)

\(x=-4950:99=-50\)

cộng cả 2 vế với -1

x=105

chỉ chi tiết giùm

a. 20-2x-8=4 => 2x=4+8-20 =>2x=-8=>x=-4

b, 2x-9-25=102 => 2x=102+25+9 => 2x=136 => x=68