\(\frac{a}{b}=\frac{c}{d}\Leftrightarrow ad=bc\)

Áp dụng kiến thức trên ta có:

\(\frac{x}{-2}=-\frac{8}{x}\Leftrightarrow x.x=\left(-8\right).\left(-2\right)=16\)

\(\Leftrightarrow x^2=16\rightarrow x\in\left\{-4;4\right\}\)

Ta có:

\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x.x=\left(-2\right).\left(-8\right)\Rightarrow x^2=16=4^4\Rightarrow x=4\)

\(\frac{x}{-2}\)= \(\frac{-8}{x}\)= x.x= -8.-2= x.x= 16=> x=4

\(\frac{3}{2}x-\frac{11}{5}=\frac{7}{8}.\frac{64}{49}\)

\(\frac{3}{2}x-\frac{11}{5}=\frac{8}{7}\)

\(\frac{3}{2}x=\frac{8}{7}+\frac{11}{5}=\frac{117}{35}\)

\(x=\frac{117}{35}:\frac{3}{2}=\frac{78}{35}\)

\(\frac{3}{2}x-\frac{11}{5}=\frac{7}{8}.\frac{64}{49}\) 

\(\frac{3}{2}x-\frac{11}{5}=\frac{8}{7}\)

\(\frac{3}{2}x=\frac{8}{7}+\frac{11}{5}\)

\(\frac{3}{2}x=\frac{117}{35}\)

\(x=\frac{117}{35}:\frac{3}{2}\)

\(x=\frac{78}{35}\)

\(\left(2\frac{1}{3}+3\frac{1}{2}\right):\left(x+3\frac{1}{7}\right)+7\frac{1}{2}=1\frac{69}{86}\)

\(\left(\frac{7}{3}+\frac{7}{2}\right):\left(x+\frac{22}{7}\right)+\frac{15}{2}=\frac{155}{86}\)

\(\left(\frac{14}{6}+\frac{21}{6}\right):\left(x+\frac{22}{7}\right)+\frac{15}{2}=\frac{155}{86}\)

 \(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{155}{86}-\frac{15}{2}\)

\(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{155}{86}-\frac{645}{86}\)

 \(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{-245}{43}\)

 \(x+\frac{22}{7}=\frac{35}{6}:\frac{-245}{43}=\frac{35}{6}\cdot\frac{-43}{245}\)

\(x+\frac{22}{7}=\frac{-43}{42}\)

\(x=\frac{-43}{42}-\frac{22}{7}=\frac{-43}{42}-\frac{132}{42}\)

 \(x=\frac{-25}{6}\)

\(\frac{-2}{3}.x+\frac{1}{5}=\frac{3}{10}\)

  \(\frac{-2}{3}.x=\frac{3}{10}-\frac{1}{5}=\frac{1}{10}\)

           \(x=\frac{1}{10}:\frac{-2}{3}=-\frac{3}{20}\)

Từ đề bài ta có:

4/3x - 1/3 = (2x-1) : 3/5 

=> 4/3x -1/3 = (2x-1) * 5/3

=> 4/3x -1/3= 10/3x - 5/3

Chuyển vế đổi dấu

Ta được:

=> -2x = -4/3

=> x= 2/3

Vậy x= 2/3

\(1\frac{1}{3}x=\left(2x-1\right):\left(1-\frac{2}{5}\right)\)

\(\frac{4}{3}x=\left(2x-1\right):\left(\frac{3}{5}\right)\)

\(\frac{4}{3}x.\frac{3}{5}=\left(2x-1\right)\)

\(\frac{4}{5}x=\left(2x-1\right)\)

\(x=\left(2x-1\right):\frac{4}{5}\)

\(x=\left(2x-1\right).\frac{5}{4}\)

\(x=2x.\frac{5}{4}-1.\frac{5}{4}\)

\(x=\)\(2x.\frac{5}{4}-\frac{5}{4}\)

\(x=2.\frac{5}{4}.x-\frac{5}{4}\)

\(x=\left(\frac{5}{2}.x\right)-\frac{5}{4}\)

\(x=\frac{5}{2}-\frac{5}{4}.x-\frac{5}{4}\)

\(x=\frac{5}{4}.x-\frac{5}{4}\)

\(x=x\left(\frac{5}{4}-\frac{5}{4}\right)\)

\(x=x.0\)

\(=>x=0\)

Ta có : \(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

<=> \(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x=-1\)

<=> \(\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)x=-1\)

<=> \(0.x=-1\)

=> x thuộc rỗng 

\(\frac{1}{6}x+\frac{1}{10}x-\frac{4}{15}x+1=0\)

\(\Leftrightarrow\left(\frac{1}{6}+\frac{1}{10}-\frac{4}{15}\right)x+1=0\)

\(\Leftrightarrow\left(\frac{5}{30}+\frac{3}{30}-\frac{8}{30}\right)x+1=0\)

\(\Leftrightarrow\frac{5+3-8}{30}x+1=0\)

\(\Leftrightarrow0x=-1\)(vô lí)

vậy không có giá trị nào của x thỏa mãn.