Ta có  \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

           \(\Rightarrow\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

                 \(2\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2}{9}\)

                 \(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

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

                 \(\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}\div2\)

                  \(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

                   \(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)

                     \(\frac{1}{x+1}=\frac{1}{18}\left(1\right)\)

                   Có \(\left(1\right)\Leftrightarrow\left(x+1\right).1=1.18\) 

                                       \(\Rightarrow x+1=18\)

                                       \(\Rightarrow x=18-1\)

                                       \(\Rightarrow x=17\)

\(\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}+...+\frac{1}{Xx\left(X+1\right)}=\frac{1}{9}\)

\(\frac{7-6}{6x7}+\frac{8-7}{7x8}+\frac{9-8}{8x9}+...+\frac{\left(X+1\right)-X}{Xx\left(X+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{X}-\frac{1}{X+1}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{X+1}=\frac{1}{9}\)

\(\frac{1}{X+1}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\)

X+1=18

X=17

y*4+y*3=644

y*7=644

y         =644/7

y         =92

a: \(8x\left(2023+x\right)-8x\left(x+2024\right)=56\)

=>\(8x\left(x+2023-x-2024\right)=56\)

=>-8x=56

=>\(x=\frac{56}{-8}=-7\) (nhận)

b: \(5-2025x=9-2026\left(x-1\right)\)

=>-2025x+5=9-2026x+2026

=>-2025x+5=-2026x+2035

=>x=2035-5=2030(nhận)

c: \(\left(-12\right)^2\cdot x=56+10\cdot13x\)

=>144x=56+130x

=>14x=56

=>x=4(nhận)

d: -(x-32+11)=(21-33-x+7)

=>-(x-21)=(-x-5)

=>-x+21=-x-5

=>21=-5(vô lý)

=>x∈∅

e: \(-2\left(x+6\right)+6\left(x+10\right)=8\)

=>-2x-12+6x+60=8

=>4x+52=8

=>4x=8-52=-44

=>\(x=-\frac{44}{4}=-11\) (nhận)

`- 9 . ( x - 6 ) + 20 = 56`

`=> -9 . ( x - 6 ) = 56-20`

`=> -9 . ( x - 6 ) =36`

`=>x-6=36:(-9)`

`=>x-6=-4`

`=>x=-4+6`

`=>x=2`

`-------------`

` ( 245 - x ) + 7^2=149`

`=>( 245 - x ) +49=149`

`=> 245 - x =149-49`

`=> 245 - x =100`

`=>x=245-100`

`=>x=145`

`------------`

`(2^x-3).7=35`

`=> 2^x-3=35:7`

`=> 2^x-3=5`

`=>2^x=5+3`

`=>2^x=8`

`=>2^x=2^3`

`=>x=3`