a: \(x\in\left\{-6;-5;-4;...;4;5\right\}\)

Tổng là -6

11(x-6)=4(x+3)-1

11x-66=4x+11

11x-4x-66=11

11x-4x=11+66

7x=77

x=11

mình bị mù nên không thấy j

tay mình gãy nên không nháp đc

\(a,-\dfrac{x}{2}+\dfrac{2x}{3}+\dfrac{x+1}{4}+\dfrac{2x+1}{6}=\dfrac{8}{3}\)

\(\Rightarrow-\dfrac{6x}{12}+\dfrac{8x}{12}+\dfrac{3\left(x+1\right)}{12}+\dfrac{2\left(2x+1\right)}{12}=\dfrac{8}{3}\)

\(\Rightarrow\dfrac{-6x+8x+3x+3+4x+2}{12}=\dfrac{8}{3}\)

\(\Rightarrow\dfrac{9x+5}{12}=\dfrac{8}{3}\)

\(\Rightarrow27x+15=96\)

\(\Rightarrow27x=81\)

\(\Rightarrow x=3\left(tm\right)\)

\(b,\dfrac{3}{2x+1}+\dfrac{10}{4x+2}-\dfrac{6}{6x+3}=\dfrac{12}{26}\)

\(\Rightarrow\dfrac{3}{2x+1}+\dfrac{10}{2\left(2x+1\right)}-\dfrac{6}{3\left(2x+1\right)}=\dfrac{6}{13}\)

\(\Rightarrow\dfrac{3}{2x+1}+\dfrac{5}{2x+1}-\dfrac{2}{2x+1}=\dfrac{6}{13}\)

\(\Rightarrow\dfrac{3+5-2}{2x+1}=\dfrac{6}{13}\)

\(\Rightarrow\dfrac{6}{2x+1}=\dfrac{6}{13}\)

\(\Rightarrow2x+1=13\)

\(\Rightarrow2x=12\)

\(\Rightarrow x=6\left(tm\right)\)

#Toru

a) \(-\dfrac{x}{2}+\dfrac{2x}{3}+\dfrac{x+1}{4}+\dfrac{2x+2}{6}=\dfrac{8}{3}\) 

\(\Rightarrow\dfrac{-6x}{12}+\dfrac{8x}{12}+\dfrac{3\left(x+1\right)}{12}+\dfrac{2\left(2x+1\right)}{12}=\dfrac{4\cdot8}{12}\)

\(\Rightarrow-6x+8x+3x+3+4x+2=32\)

\(\Rightarrow9x+5=32\)

\(\Rightarrow9x=32-5\)

\(\Rightarrow9x=27\)

\(\Rightarrow x=\dfrac{27}{9}\)

\(\Rightarrow x=3\)

b) \(\dfrac{3}{2x+1}+\dfrac{10}{4x+2}-\dfrac{6}{6x+3}=\dfrac{12}{26}\) (ĐK: \(x\ne-\dfrac{1}{2}\)) 

\(\Rightarrow\dfrac{3}{2x+1}+\dfrac{10}{2\left(2x+1\right)}-\dfrac{6}{3\left(2x+1\right)}=\dfrac{6}{13}\)

\(\Rightarrow\dfrac{3}{2x+1}+\dfrac{5}{2x+1}-\dfrac{2}{2x+1}=\dfrac{6}{13}\)

\(\Rightarrow\dfrac{6}{2x+1}=\dfrac{6}{13}\)

\(\Rightarrow2x+1=13\)

\(\Rightarrow2x=12\)

\(\Rightarrow x=\dfrac{12}{2}\)

\(\Rightarrow x=6\left(tm\right)\)

5x+6⋮x+2

=>5(x+2)-4⋮x+2

Mà x+2⋮x+2 =>5(x+2)⋮x+2

=>4⋮x+2

=>x+2∈Ư(4)={-4;-2;-1;1;2;4}

=>x∈{-6;-4;-3;-1;0;2}

Vì x+2 ⋮ x+2; 5 ∈ N

=> 5(x+2) ⋮ x+2

=> 5x +10 ⋮ x+2

Mà 5x + 6 ⋮ x+2

=> (5x+10)-(5x+6) ⋮ x+2

=> 4 ⋮ x+2

=> x+2 thuộc tập ước của 4

Mà ước của 4 = {1;-1;2;-2;4;-4}

=> x+2 ∈ {1;-1;2;-2;4;-4}

=> x ∈ {-1;-3;0;-4;2;-6}

Vậy x ∈ {-1;-3;0;-4;2;-6}

a: =>2x-x=-5/2-1/3

=>x=-17/6

b: =>4(x-2)²=36

=>(x-2)²=9

=>x-2=3 hoặc x-2=-3

hay x=5 hoặc x=-1

c: =>2x+1/2=5/6

=>2x=1/3

hay x=1/6

a: =>2x-x=-5/2-1/3

=>x=-17/6

b: =>4(x-2)²=36

=>(x-2)²=9

=>x-2=3 hoặc x-2=-3

hay x=5 hoặc x=-1

c: =>2x+1/2=5/6

=>2x=1/3

hay x=1/6

a) \(\left(x+\frac{1}{2}\right).\left(\frac{2}{3}-2x\right)=0\)

\(\Rightarrow x+\frac{1}{2}=0\)                                              \(\Rightarrow\frac{2}{3}-2x=0\)

\(x=\frac{-1}{2}\)                                                                         \(2x=\frac{2}{3}\)

                                                                                                  \(x=\frac{2}{3}:2\)

                                                                                                 \(x=\frac{1}{3}\)

KL: x = -1/2 hoặc x= 1/3

b) \(\left|2x-\frac{1}{3}\right|+\frac{5}{6}=\frac{11}{6}\)

\(\left|2x-\frac{1}{3}\right|=1\)

TH1: \(2x-\frac{1}{3}=1\)

         \(2x=\frac{4}{3}\)

             \(x=\frac{2}{3}\)

TH2: \(2x-\frac{1}{3}=-1\)

\(2x=\frac{-2}{3}\)

\(x=\frac{-2}{3}:2\)

\(x=\frac{-1}{3}\)

KL: x =.........

Học tốt nhé bn!!!

2+4+6+8+.....+2.x=210

=>2.1+2.2+2.3+2.4+.....+2.x=210

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

=2.[x.(x+1)/2]=210

=>x.(x+1)=210

=>x.(x+1)=14.(14+1)

suy ra x=14

học tốt nhé bn

\(2+4+6+8+...+2x=210\)

\(\frac{(2\chi+2)\times\chi}{2}=210\)

\(2\left(x+1\right)x=210\cdot2=420\)

\(x\left(x+1\right)=420:2=210\)

\(x=14\)

2+ 4+ 6+...+( 2X- 2)+ 2X= 210.

=> 2[ 1+ 2+ 3+...+( X- 1)+ X]= 210.

=> 1+ 2+ 3+...+( X- 1)+ X= 210: 2.

=> 1+ 2+ 3+...+( X- 1)+ X= 105.

=>( X+ 1)x X: 2= 105.

=>( X+ 1)x X= 105x 2.

=>( X+ 1)x X= 210.

=>( X+ 1)x X= 15. 14.

=> X= 14.

Vậy X= 14.