1: \(\left(x-3\right)\left(2x-5\right)-3x\left(x+4\right)\)

\(=2x^2-5x-6x+15-3x^2-12x\)

\(=-x^2-23x+15\)

2: \(\left(\dfrac{1}{2}x+5\right)\left(2x-\dfrac{1}{5}\right)\)

\(=x^2-\dfrac{1}{10}x+10x-1\)

\(=x^2+\dfrac{99}{10}x-1\)

\(\frac{3x}{2\cdot5}+\frac{3x}{5\cdot8}+\frac{3x}{8\cdot11}+\frac{3x}{11\cdot14}=\frac{1}{21}\)

\(=>\frac{3x}{3}\left[\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\right]=\frac{1}{21}\)

\(=>x\left[\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\right]=\frac{1}{21}\)

\(=>x\left[\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{11}-\frac{1}{14}\right]=\frac{1}{21}\)

\(=>x\left[\frac{1}{2}-\frac{1}{14}\right]=\frac{1}{21}\)

\(=>x\cdot\frac{3}{7}=\frac{1}{21}\Leftrightarrow x=\frac{1}{9}\)

\(\left(3x-1\right)\left(2x+7\right)-\left(x+1\right)\left(6x-5\right)=16\)

\(\Rightarrow6x^2-19x-7-6x^2-x+5=16\)

\(\Rightarrow-20x=18\Rightarrow x = -\frac{9}{10}\)

xong rùi nha ^^ 

x + 2x + 3x + ... + 99x = 2 + 4 + 6 + 198 (có 99 số hạng)

x + 2x + 3x + ... + 99x = (198 + 2) . 99 : 2 

x .(1 + 2 + 3 + ... + 99) = 9900

x .  [(99 + 1) . 99 : 2]    = 9900

x . 4950                      = 9900

x                                = 9900 : 4950

x                                = 2

x+2x+3x+....+99x=2+4+6+..+198

x(1+2+3+4+...+99)=9900

x=9900/4950

x=2

x + 2x + 3x + 4x + ...... + 99x = 2 + 4 + 6 + 8 + ..... + 198

x.(1 + 2 + 3 + 4 + 5 + ...... + 99) = 2 + 4 + 6 + 8 + ..... + 198 

Ta đưa (1 + 2 + 3 + 4 + 5 + ...... + 99) ; (2 + 4 + 6 + 8 + ..... + 198)  về công thức tính dãy số

=> 1 + 2 + 3 + 4 + 5 + ...... + 99 = 1950

=>  2 + 4 + 6 + 8 + ..... + 198 = 9900

=> x.4950 = 9900

=> x = 2

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

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

\(\frac{9}{5}.\left(x-1\right)=\frac{-1}{2}-\frac{2}{5}\)

\(\frac{9}{5}.\left(x-1\right)=\frac{-9}{10}\)

\(x-1=\frac{-9}{10}:\frac{9}{5}\)

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

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

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

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

\(\frac{3}{5}\left(3x-3\right)=-\frac{5}{10}-\frac{2}{5}\)

\(\frac{3}{5}\left(3x-3\right)=-\frac{9}{10}\)

\(\left(3x-3\right)=-\frac{9}{10}:\frac{3}{5}\)

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

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

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

Vậy...

2/5+3/5.(3x-3)=(-5/10)

3/5.(3x-3)=(-5/10)-2/5

3/5.(3x-3)=(-9/10)

3x-3=(-9/10):3/5

3x-3=(-3/2)

3x=(-3/2)+3

3x=3/2

x=1/2

1)    \(\frac{2}{3}x+\frac{3}{4}\left(x-5\right)=-\frac{5}{6}\)

      \(\frac{2}{3}x+\frac{3}{4}x-\frac{15}{4}=-\frac{5}{6}\)

       \(\frac{17}{12}x=-\frac{5}{6}+-\frac{15}{4}=-\frac{55}{12}\)

   \(x=-\frac{55}{12}:\frac{17}{12}=-\frac{55}{17}\)

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

=> x(0,5 - 2/3) = 5/12

=> -1/6x = 5/12

=> x = (5/12) / (-1/6)

=> x = -5/2 

2.(5+3x)+x=31

10+6x+x    =31

7x              =21

  x              = 3

2.(5+3x)+x=31

=> 10+6x+x=31

=>10+7x=31

=>7x=31-10=21

=>x=3 

#HọcTốt

2.(5+3x)+x=31

10+6x+x=31 

10+7x=31

  7x=  31-10

7x  =21 

x=21:7

x=3

Nếu x,y thuộc Z 
suy ra phương trình tương đương với y(4-x)-3(4-x)=15-12 
suy ra (4-x)(y-3)=3 
Xét các trường hợp 
4-x=1 thì y-3=3 
4-x=-1 thì y-3= -3 
4-x =3 thì y-3=1 
4-x= -3 thì y-3= -1 
giải các trường hợp ra tìm x và y