Câu a:

- \(\frac12\)(3 - 2\(x\)) - 7 = 5 - \(\frac13\)(\(x\) - \(\frac45\))

- \(\frac32\) + \(x\) - 7 = 5 - \(\frac13x\) + \(\frac{4}{15}\)

\(x\) + \(\frac13x\) = 5 + \(\frac{4}{15}\) + 7 + \(\frac32\)

(1 + \(\frac13\))\(x\) = \(\frac{150}{30}\) + \(\frac{8}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{158}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{368}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{413}{30}\)

\(x\) = \(\frac{413}{30}\) : \(\frac43\)

\(x\) = \(\frac{413}{40}\)

Vậy \(x=\frac{413}{40}\)

Câu b:

(5 - 3x/2) : - 1 3/8 = - 7 1/3

(5 - 3x/2) : (-11/8) = - 22/3

5 - 3x/2 = - 22/3 x (-11/8)

5 - 3x/2 = 121/12

3x/2 = 5 - 121/12

3x/2 = - 61/12

x = - 61/12 : 3/2

x = -61/18

Vậy x = - 61/18

Câu a:

\(\frac{-8}{3x-1}\) = \(\frac{4}{-7}\)

-8.(-7) = 4.(3\(x\) - 1)

56 = 12\(x\) - 4

12\(x\) = 56+ 4

12\(x\) = 60

\(x\) = 60 : 12

\(x\) = 5

Vậy \(x\) = 5

Câu b:

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

\(x^2\) = (-3)\(^2\)

\(\left[\begin{array}{l}x=-3\\ x=3\end{array}\right.\)

Vậy \(x\in\left\lbrace-3;3\right\rbrace\)

Câu c:

\(-\frac{4}{y}=\frac{x}{2}\)

-4.2 = \(x.y\)

\(xy=-8\)

Ư(8) = (-8; -4; -2; -1; 1; 2; 4; 8}

Vậy (\(x;y\)) = (-8; 1); (-4; 2); (-2; 4); (-1; 8); (1; -8); (2; -4); (4; -2); (8; -1)

Câu 2:

(\(x-1)\)(y + 2) = 7

Ư(7) = {-7; -1; 1; 7}

Lập bảng ta có:

Theo bảng trên ta có:

(\(x;y\)) = (-6; -3); (0; -9); (2; 5); (8; - 1)

Vậy (\(x;y\)) = (-6; -3); (0; -9); (2; 5); (8; -1)

Bài 1 : Ta có:

\(\frac{7+\frac{7}{11}+\frac{7}{23}+\frac{7}{31}}{9+\frac{9}{11}+\frac{9}{23}+\frac{9}{31}}\)

= \(\frac{7.\left(1+\frac{1}{11}+\frac{1}{23}+\frac{1}{31}\right)}{9.\left(1+\frac{1}{11}+\frac{1}{23}+\frac{1}{31}\right)}\)

= \(\frac{7}{9}\)

Bài 2 :

 \(\frac{x}{2}+\frac{3x}{4}+\frac{5x}{6}=\frac{10}{24}\)

=> \(\frac{12x+18x+20x}{24}=\frac{10}{24}\)

=> 50x = 10

=> x = 10 : 50

=> x = 1/5

Bài 3 : Để A nhận giá trị nguyên thì 3 \(⋮\)x + 3

                                         <=> x + 3 \(\in\)Ư(3) = {1; -1; 3; -3}

Lập bảng :

Vậy 

0,5x-2/3x=7/12

=>(1/2-2/3).x=7/12

=>-1/6x=7/12

=>x=7/12:1/6

=>x=7/2

b, x:4 1/3=-2,5

=>x:13/3=-2,5

=>x=-5/2x13/3

=>x=-13

c,5,5x=13/15

=>11/2x=13/15

=>x=13/15:11/2

=>x=26/165

d,(3x/7+1):-4=-1/28

=>3x/7+1=-1/28x(-4)

=>3x/7+1=-1/7

=>3x/7=-1/7-1

=>3x/7=-8/7

=>3x=-8/7x7

=>3x=8

=>x=8:3

=>x=8/3

\(0,5x-\frac{2}{3}x=\frac{7}{12}\)

\(\frac{1}{2}x-\frac{2}{3}x=\frac{7}{12}\)

\(\left(\frac{1}{2}-\frac{2}{3}\right)x=\frac{7}{12}\)

\(\frac{-1}{6}x=\frac{7}{12}\)

\(x=-21\)

b,c,d tương tự

a, \(\frac{17}{y}=\frac{-7}{11}\)

\(\Rightarrow17\cdot11=-7\cdot y\)

\(\Rightarrow187=-7\cdot y\)

\(\Rightarrow\frac{187}{-7}=y\)

b, \(\frac{-8}{3x-1}=\frac{4}{7}\)

\(\Rightarrow\frac{-8}{3x-1}=\frac{-8}{-14}\)

\(\Rightarrow3x-1=-14\)

\(\Rightarrow3x=-14+1\)

\(\Rightarrow3x=-13\)

\(\Rightarrow x=\frac{-13}{3}\)

c, \(\frac{x}{-3}=\frac{-3}{x}\)

\(\Rightarrow x\cdot x=-3\cdot\left(-3\right)\)

\(\Rightarrow x^2=9\)

\(\Rightarrow x^2=\left(\pm3\right)^2\)

\(\Rightarrow x=\pm3\)

d, \(\frac{-4}{y}=\frac{x}{2}\)

\(\Rightarrow-4\cdot2=x\cdot y\)

\(\Rightarrow-8=x\cdot y\)

\(\Rightarrow x;y\inƯ\left(-8\right)=\left\{-1;1;-2;2;-4;4;-8;8\right\}\)

ta có bảng :

a)\(\frac{14}{y}\)\(=\)   \(\frac{-7}{11}\)

\(\Rightarrow\)\(14\cdot11=y\cdot\left(-7\right)\)

                   \(y=\)\(\frac{14\cdot11}{-7}\)

                   \(y=22\)

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

\(\Rightarrow\) \(x\cdot x=\left(-3\right)\cdot\left(-3\right)\)

\(\Rightarrow\)\(x^2=9\)

\(\Rightarrow\)\(x^2=9\)hoặc  \(x^2=-9\)

\(TH1:\) \(x^2=9\)

     \(\Rightarrow\)\(x=3\)

\(TH2:\)\(x^2=-9\)

     \(\Rightarrow\)\(x=-3\)

\(\left|x+\frac{7}{3}\right|=\left|x-\frac{7}{2}\right|\)

Vì \(x+\frac{7}{3}\ne x-\frac{7}{2}\)nên \(x+\frac{7}{3}=\frac{7}{2}-x\)

\(\Leftrightarrow x+x=\frac{7}{2}-\frac{7}{3}\)

\(\Leftrightarrow2x=\frac{21}{6}-\frac{14}{6}\)

\(\Leftrightarrow2x=\frac{7}{6}\)

\(\Leftrightarrow x=\frac{7}{6}\div2\)

\(\Leftrightarrow x=\frac{7}{12}\)

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

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

\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{1}{3}=-2x\\2x-\frac{1}{3}=2x\end{cases}}\Leftrightarrow\orbr{\begin{cases}4x=\frac{1}{3}\\x\in\left\{\varnothing\right\}\end{cases}}\Leftrightarrow x=\frac{1}{12}\)

Vậy \(x=\frac{1}{12}\)

a, -3/4-2x= 4

 2x=-19/4

x=-19/8

(-2/3x-3/5).(-29/6)=2/5

-2/3x-3/5=-12/145

-2/3x=15/29

x=-45/58

\(\frac{11}{4}:\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{7}{2}\)

\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{4}:\frac{7}{2}\)

\(\Leftrightarrow\frac{3}{2}:\left|4x-\frac{1}{3}\right|=\frac{11}{14}\)

\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{3}{2}:\frac{11}{14}\)

\(\Leftrightarrow\left|4x-\frac{1}{3}\right|=\frac{21}{11}\)

\(\Leftrightarrow\orbr{\begin{cases}4x-\frac{1}{3}=\frac{21}{11}\\4x-\frac{1}{3}=-\frac{21}{11}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{37}{66}\\x=-\frac{13}{33}\end{cases}}\)

Bài dưới tương tự

\(\frac{3}{x-5}=-\frac{4}{x+2}\)

\(\Leftrightarrow3\left(x+2\right)=\left(-4\right)\left(x-5\right)\)

\(\Leftrightarrow3x+6=-4x+20\)

\(\Leftrightarrow7x=14\)

\(\Leftrightarrow x=2\)

\(\frac{4}{x+2}=\frac{7}{3x+1}\)

\(\Leftrightarrow4\left(3x+1\right)=\left(x+2\right)7\)

\(\Leftrightarrow12+4=7x+14\)

\(\Leftrightarrow5x=10\)

\(\Leftrightarrow x=2\)

\(-\frac{3}{x+1}=\frac{4}{2-2x}\)

\(\Leftrightarrow\left(-3\right)\left(2-2x\right)=\left(x+1\right)4\)

\(\Leftrightarrow-6+6x=4x+4\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\)

=5 Nha