37 - 5 x 5 = 12 : Đ

180 : 6 + 30 = 60 : Đ

30 + 60 x 2 = 150 : Đ

282 - 100 : 2 = 91 : S

Bài làm:

1) đk: \(x\ne0;x\ne-5\)

Ta có: \(\frac{30}{x}-\frac{30}{x+5}=1\)

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

\(\Leftrightarrow x^2+5x=150\)

\(\Leftrightarrow x^2+5x-150=0\)

\(\Leftrightarrow\left(x-10\right)\left(x+15\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-10=0\\x+15=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=10\\x=-15\end{cases}}\)

2) đk: \(x\ne0;x\ne-2\)

Ta có: \(\frac{60}{x}-\frac{60}{x+2}=1\)

\(\Leftrightarrow\frac{60\left(x+2\right)-60x}{x\left(x+2\right)}=1\)

\(\Leftrightarrow x^2+2x=120\)

\(\Leftrightarrow x^2+2x-120=0\)

\(\Leftrightarrow\left(x-10\right)\left(x+12\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-10=0\\x+12=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=10\\x=-12\end{cases}}\)

\(\frac{30}{x}-\frac{30}{x+5}=1\)( ĐKXĐ : \(x\ne0;x\ne-5\))

<=> \(30\left(\frac{1}{x}-\frac{1}{x+5}\right)=1\)

<=> \(30\left(\frac{x+5}{x\left(x+5\right)}-\frac{x}{x\left(x+5\right)}\right)=1\)

<=> \(30\left(\frac{5}{x\left(x+5\right)}\right)=1\)

<=> \(\frac{5}{x\left(x+5\right)}=\frac{1}{30}\)

<=> \(5\cdot30=x\left(x+5\right)\)

<=> \(x^2+5x-150=0\)

<=> \(x^2+15x-10x-150=0\)

<=> \(x\left(x+15\right)-10\left(x+15\right)=0\)

<=> \(\left(x-10\right)\left(x+15\right)=0\)

<=> \(\orbr{\begin{cases}x-10=0\\x+15=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-15\end{cases}}\)( tmđk )

Vậy S = { 10 ; -15 }

\(\frac{60}{x}-\frac{60}{x+2}=1\)( ĐKXĐ : \(x\ne0;x\ne-2\))

<=> \(60\left(\frac{1}{x}-\frac{1}{x+2}\right)=1\)

<=> \(60\left(\frac{x+2}{x\left(x+2\right)}-\frac{x}{x\left(x+2\right)}\right)=1\)

<=> \(60\left(\frac{2}{x\left(x+2\right)}\right)=1\)

<=> \(\frac{2}{x\left(x+2\right)}=\frac{1}{60}\)

<=> \(2\cdot60=x\left(x+2\right)\)

<=> \(x^2+2x-120=0\)

<=> \(x^2+12x-10x-120=0\)

<=> \(x\left(x+12\right)-10\left(x+12\right)=0\)

<=> \(\left(x-10\right)\left(x+12\right)=0\)

<=> \(\orbr{\begin{cases}x-10=0\\x+12=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=10\\x=-12\end{cases}}\)

Vậy S = { 10 ; -12 }

D

D

a) 2x - 20 = x + 30

2x - x = 30 + 20

x = 50

b) 5x - 30 + 4x = 60

9x = 60 + 30

9x = 90

x = 90 : 9

x = 10

a) 2x - 20 = x + 30

2x - x = 30 + 20

x = 50

b) 5x - 30 + 4x = 60

9x = 60 + 30

9x = 90

x = 90 : 9

x = 10

D

D

a/30.x=2280040
   30.x=570
       x=570:30=19
b/(x.30):40=840
    x.30     =840.40
    x.30     =33600
    x         =33600:30=1120
c/37200:x=60.5
  37200:x=300
            x=37200:300=124
d/(72000:x):60=5
    72000:x     =5.60
    72000:x     =300
              x     =72000:300=240

a, 245 - 5 . ( 16 + x ) = 140

              5 . ( 16 + x ) = 245 - 140

              5  . ( 16 + x ) = 145

                     16 + x     = 145 : 5

                     16 + x     = 29 

                             x      = 29 - 16

                             x      = 13 .

b, ( x - 1945 ) . 5  = 50

     x - 1945           = 50 : 5

     x - 1945           = 10

            x                = 10 + 1945

           x                 = 1955 .

c, 30 . ( 60 - x ) = 30

            60 - x     = 30 : 30

           60 - x      = 1

                  x       = 60 - 1

                  x       = 59 .

d, [ ( 250 - 25 ) : 15 ] : x = ( 450 - 60 ) : 130

    [ 225 : 15 ]             : x  = 390 : 130

       15                        : x  =  3

                                     x  = 15 : 3

                                     x  = 5 .

e, x : [ ( 1800 + 600 ) ] = 560 : ( 315 - 35 )

    x : 2400                     = 560 : 280

    x : 2400                     = 2

    x                                 = 2 . 2400

    x                                 = 4800 .

f, x . ( x + 1 ) = 2 + 4 + 6 + 8 + 10 + ... + 2500

2 + 4 + 6 + 8 + 10 + ... + 2500

 Số số hạng của dãy số trên là :

       ( 2500 - 2 ) : 2 + 1 = 1250 ( số hạng )

=> 2 + 4 + 6 + 8 + 10 + 2500

= ( 2 + 2500 ) . 1250 : 2

= 2502 . 1250 : 2

= 3127500 : 2

= 1563750 .

Ta có :

x . ( x + 1 ) = 1563750

Mà : 1563750 = 1250 . 1251

=> x = 1250 .

gõ latex đi bn!

a. 2^x + 70 = 74

<=> 2^x = 4

<=> x = 2

b. 120 - \(\dfrac{4x}{2}\) = 80

<=> 120 - 2x = 80

<=> 120 - 80 = 2x

<=> 2x = 40

<=> x = 20

c. (3x + 5)² = 400

<=> \(|3x+5|=\sqrt{400}\)

<=> \(|3x+5|=20\)

<=> \(\left[{}\begin{matrix}3x+5=20\\3x+5=-20\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{-25}{3}\end{matrix}\right.\)