- Mình có thể giúp bài 1 :)

 5^x +  5^ ( x + 2 ) = 650

5^x +  5^x . 5² = 650

 5^x .( 1 + 25 ) = 650

 5^x . 26 = 650 

5^x = 650 : 26

 5^x = 25

 5^x = 5² 

=> x = 2 

Vậy x = 2 

\(\dfrac{3x-5}{7}=\dfrac{2x+1}{13}\)

Ta có: \(\left(3x-5\right).13=\left(2x+1\right).7\)

\(=>39x-65=14x+7\)

\(=>39x-14x=7+65\)

\(=>25x=72\)

\(=>x=72:25\)

Vậy \(x=\dfrac{72}{25}\)

_{(* Công thức: Hai phân số bằng nhau thì hai nhân chéo cũng bằng nhau )}

(3x - 5)/7 = (2x + 1)/13

13.(3x - 5) = 7.(2x + 1)

39x - 65 = 14x + 7

39x - 14x = 7 + 65

25x = 72

x = 72/25

Bài làm:

a) \(\left(\frac{2x}{7}-5\right)\div\left(-8\right)=0,75\)

\(\Leftrightarrow\frac{2x}{7}-5=-6\)

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

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

b) \(\frac{11}{13}-\left(\frac{5}{42}-x\right)=-\left(\frac{15}{28}-\frac{11}{13}\right)\)

\(\Leftrightarrow x+\frac{11}{13}-\frac{5}{42}=\frac{11}{13}-\frac{15}{28}\)

\(\Rightarrow x=-\frac{5}{7}\)

Vậy không có x nào thỏa mãn

Lời giải:

a) 

$1+3+5+...+(2x-1)=750$

$\frac{(2x-1+1)x}{2}=750$

$x^2=750$

$x=\sqrt{750}$ (vô lý?!!)

b) 

$1+5+9+13+...+x=501501$

$\frac{1}{2}(\frac{x-1}{4}+1)(x+1)=501501$

$(x+1)(x+3)=4012008$$x(x+4)=4012005=2001.2005$

$\Rightarrow x=2001$

a)

 13/4+x=2

          x=2-13/4

         x=-5/4

b)

 2x.17/12=3/7

 2x          =3/7;17/12

 2x         =36/119

  x           =36/119 : 2

  x           =18/119

c)

 2x.17/12=19/7

 2x         =19/7:17/12

 2x         =228/119

   x         =228/119;2

   x         =114/119

d)

 1/2x + 5/6=-3

 1/2x         =-3-5/6

 1/2x         =-23/6

     x          =-23/6:1/2

    x          =-23/3

\(a,3\left(2x-3\right)+2\left(2-x\right)=-3\\ \Leftrightarrow6x-9+4-2x=-3\\ \Leftrightarrow4x=2\\ \Leftrightarrow x=\dfrac{1}{2}\\ b,x\left(5-2x\right)+2x\left(x-1\right)=13\\ \Leftrightarrow5x-2x^2+2x^2-2x=13\\ \Leftrightarrow3x=13\\ \Leftrightarrow x=\dfrac{13}{3}\\ c,5x\left(x-1\right)-\left(x+2\right)\left(5x-7\right)=6\\ \Leftrightarrow5x^2-5x-5x^2-3x+14=6\\ \Leftrightarrow-8x=-8\\ \Leftrightarrow x=1\\ d,3x\left(2x+3\right)-\left(2x+5\right)\left(3x-2\right)=8\\ \Leftrightarrow6x^2+9x-6x^2-11x+10=8\\ \Leftrightarrow-2x=-2\\ \Leftrightarrow x=1\)

\(e,2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\\ \Leftrightarrow10x-16-12x+15=12x-16+11\\ \Leftrightarrow-14x=-4\\ \Leftrightarrow x=\dfrac{2}{7}\\ f,2x\left(6x-2x^2\right)+3x^2\left(x-4\right)=8\\ \Leftrightarrow12x^2-4x^3+3x^3-12x^2=8\\ \Leftrightarrow-x^3-8=0\\ \Leftrightarrow-\left(x^3+8\right)=0\\ \Leftrightarrow-\left(x+2\right)\left(x^2-2x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x\in\varnothing\left(x^2-2x+4=\left(x-1\right)^2+3>0\right)\end{matrix}\right.\)

Bài 4:

a: Ta có: \(3\left(2x-3\right)-2\left(x-2\right)=-3\)

\(\Leftrightarrow6x-9-2x+4=-3\)

\(\Leftrightarrow4x=2\)

hay \(x=\dfrac{1}{2}\)

b: Ta có: \(x\left(5-2x\right)+2x\left(x-1\right)=13\)

\(\Leftrightarrow5x-2x^2+2x^2-2x=13\)

\(\Leftrightarrow3x=13\)

hay \(x=\dfrac{13}{3}\)

c: Ta có: \(5x\left(x-1\right)-\left(x+2\right)\left(5x-7\right)=6\)

\(\Leftrightarrow5x^2-5x-5x^2+7x-10x+14=6\)

\(\Leftrightarrow-8x=-8\)

hay x=1

a) 2x - 7 = 15 - (2 - 3x)

=> 2x - 7 = 15 - 2 + 3x

=> 2x - 7 = 13 + 3x

=> 2x - 3x = 13 + 7

=> -1x = 20

=> x = -20 thuộc Z

vậy______

b) 8 - ( x + 2 ) + ( 2x - 1 ) = 15 - ( 24 - 85 )

=> 8 - x - 2 + 2x - 1 = 15 - (-61)

=> (-x + 2x) + 8 - 2 - 1 = 76

=> 1x + 5 = 76

=> x = 76 - 5

=> x = 71 thuộc Z

vậy_____

c) -( 4x + 7 ) - ( 5 - 2x ) = 13 - x

=> -4x - 7 - 5 + 2x = 13 - x

=> (-4x + 2x) - 7 - 5 = 13 - x

=> -2x - 12 = 13 - x

=> -2x + x = 13 + 12

=> -1x = 25

=> x = - 25 thuộc Z

vậy____

a) 2x -7 = 15 - (2- 3x)

  2x - 7 = 15 - 2 +3x

  2x -3x = 15 - 2 + 7

  x( 2- 3) = 20

  -1x       = 20 

  x          = - 20