\(\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+...+\frac{1}{\left(2x-2\right)\cdot2x}=\frac{1}{8}\)

\(\Rightarrow\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+...+\frac{2}{\left(2x-2\right)\cdot2x}=\frac{2}{8}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2x-2}-\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2x}=\frac{1}{2}-\frac{1}{4}\)

\(\Rightarrow\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=2\)

\(\frac{1}{2.4}\)\(\)

1/(2.4) + 1/(4.6) + … + 1/[(2x – 2).2x] = 1/8
suy ra 2/(2.4) + 2/(4.6) + ...+ 2/[(2x - 2).2x] = 2/8
suy ra 1-1/4+1/4-1/6+...+1/(2x-2) - 1/2x = 2/8
suy ra 1 - 1/2x = 2/8
suy ra 1/2x = 1 - 2/8
suy ra 1/2x = 6/8 = 3/4
suy ra 1.4 = 2.x.3
suy ra 4 = 6x
suy ra x thuộc rỗng
 Vậy x thuộc rỗng
k cho mình nha. Chúc bạn học tốt!

Thanks you so much.

a. 20 + 8.(x + 3) = 5² . 4

8.(x + 3)             = 100 - 20

x + 3                  = 80 : 8

x                        = 10 - 3

x                        = 7

b. 120 + |x| = 150

|x|               = 150 - 120

|x|               = 30

x                 = + 30

a) 20 + 8(x + 3) = 5² . 4

 20 + 8(x + 3) = 100

8(X + 3) = 100 - 20

8(x + 3) = 80

x + 3 = 80 : 8

 x + 3 = 10

x = 10 - 3

x = 7

b) 120 + |x| = 150

|x| = 150 - 120

|x| = 30

=> \(\orbr{\begin{cases}x=30\\x=-30\end{cases}}\)

\(\left(9!-8!\right).7!.x=1^2.2^2.3^2.4^2.....8^2\)

\(\Leftrightarrow\)\(8!\left(9-1\right).7!.x=\left(1.2.3.4.....8\right).\left(1.2.3.4.....8\right)\)

\(\Leftrightarrow\)\(8!.8.7!.x=8!.8!\)

\(\Leftrightarrow\)\(8!.8!.x=8!.8!\)

\(\Leftrightarrow\)\(x=\frac{8!.8!}{8!.8!}\)

\(\Leftrightarrow\)\(x=1\)

Vậy \(x=1\)

\(\left(9!-8!\right).7!.x=1^2.2^2.3^2.4^2.....8^2\)

\(\Leftrightarrow\)\(8!\left(9-1\right).7!.x=\left(1.2.3.4.....16\right).\left(1.2.3.4.....16\right)\)

\(\Leftrightarrow\)\(8!.8.7!.x=8!.8!\)

\(\Leftrightarrow\)\(8!.8!.x=8!.8!\)

\(\Leftrightarrow\)\(x=\frac{8!.8!}{8!.8!}\)

\(\Leftrightarrow\)\(x=1\)

Vậy \(x=1\)

Vậy 

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{\left(2x-2\right).2x}=\frac{1}{8}\)

\(\Rightarrow\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{\left(2x-2\right).2x}\right)=\frac{1}{8}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2x-2}-\frac{1}{2x}=\frac{1}{8}:\frac{1}{2}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2x}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\)

\(\Leftrightarrow2x=4\)

\(\Leftrightarrow x=2\)

TL:
\(\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{\left(2x-2\right)2x}\right)=\frac{1}{8}\)  

\(\frac{1}{2}-\frac{1}{4x}=\frac{1}{8}\) 

\(\frac{1}{4x}=\frac{3}{8}\) 

=>x=2/3

hc tốt

\(a,60-3.\left(x-2\right)=51\)

               \(3.\left(x-2\right)=60-51\)

               \(3.\left(x-2\right)=9\)

           c            \(x-2=9:3\)

                         \(x-2=3\)

                                 \(x=3+2\)

                                 \(x=5\)

\(b,541+\left(218-x\right)=725\)

                       \(218-x=725-541\)

                       \(218-x=184\)

                                     \(x=218-184\)

                                     \(x=34\)

\(c,3.\left(5x-13\right)=3^4\)

    \(3.\left(5x-13\right)=81\)

             \(5x-13=81:3\)

             \(5x-13=27\)

                        \(5x=27+13\)

                        \(5x=40\)

                           \(x=8\)

\(d,\left(2x-7\right)-\left(x+135\right)=0\)

               \(2x-7-x-135=0\)

                                  \(x-142=0\)

                                                \(x=0+142\)

                                                \(x=142\)

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{\left(2x-2\right).2x}\)= \(\frac{1}{8}\)

\(\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{\left(2x-2\right).2x}\right)\)= \(\frac{1}{8}\)

\(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2x}\right)\)= \(\frac{1}{8}\)

=> \(\frac{1}{2}-\frac{1}{2x}\)= \(\frac{1}{4}\)

=> 1/2x = 1/4

=> 2x = 4

x = 4 : 2

x = 2

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{\left(2x-2\right)2x}=\frac{1}{8}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2x-2}-\frac{1}{2x}\right)=\frac{1}{8}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{2x}=\frac{1}{8}.2=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2x}=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\)

\(\Rightarrow2x=4\Leftrightarrow x=2\)

\(x+\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}=1\)

\(x+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}=1\)

\(x+1-\frac{1}{16}=1\)

\(x+\frac{15}{16}=1\)

\(x=1-\frac{15}{16}\)

\(x=\frac{1}{16}\)