\(S=2.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{29.32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(S=1-\frac{1}{16}< 1\)

Vậy \(S< 1\)

bn ê .; là j vậy

1b)\(\frac{7}{19}x\frac{8}{11}+\frac{3}{11}:\frac{19}{7}-\frac{2}{-19}=\frac{7}{19}x\frac{8}{11}+\frac{3}{11}x\frac{7}{19}+\frac{2}{19}=\left(\frac{8}{11}+\frac{3}{11}\right)\frac{7}{19}+\frac{2}{19}=\frac{7}{19}+\frac{2}{19}=\frac{9}{19}\)

c)\(4\left(\frac{4}{9}+\frac{7}{11}-\frac{4}{9}\right)=4\frac{7}{11}\)

từ rồi làm tiếp

2)

a)\(\frac{5}{6}-x=-\frac{5}{12}-\frac{1}{-4}=-\frac{5}{12}+\frac{1}{4}=-\frac{5}{12}+\frac{3}{12}=-\frac{1}{6}.\)

\(x=\frac{5}{6}--\frac{1}{6}=\frac{5}{6}+\frac{1}{6}=1\)

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

\(\frac{\left(x-2\right)\left(-7\right)}{35}=\frac{30}{35}\)

\(\Rightarrow\left(x-2\right)\left(-7\right)=30\)

c)\(\frac{1}{2}x-\frac{3}{4}x=-\frac{5}{6}\)

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

\(-\frac{1}{4}x=-\frac{5}{6}\)

\(x=\frac{20}{6}=\frac{10}{3}\)

vậy \(x=\frac{10}{3}\)

Bài 5 :

S = 1 + 3 - 5 - 7 + 9 + 11 - ... - 397 - 399

S = 1 + (3 - 5 - 7 + 9) + (11 - 13 - 15 + 17) + ... + (387 - 389 - 391 + 393) + (395 - 397 - 399)

S = 1 + 0 + 0 + ... + 0 + (- 401)

S = 1 - 401

S = - 400

Bài 5

A= 1+3-5-7+9+11-13-15+...-397-399

A= ( 1+3-5-7)+( 9+11-13-15)+...+( 393+395-397-399)

A= -8 -8 -...-8

A = -8.50 ( từ 1 đến 399 có 200 số, chia làm 4 cặp)

A= -400

Bài 6: 

b) Ta có: x(3x+9)=0

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3x+9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\3x=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)

Vậy: S={0;-3}

c) Ta có: 52-(x+21)=19-x

\(\Leftrightarrow52-x-21-19+x=0\)

\(\Leftrightarrow12=0\)(vô lý)

Vậy: \(x\in\varnothing\)

Bài 2:

a: 2/6x5/3=10/18=5/9

b: 11/9x5/10=55/90=11/18

c: 3/9x6/8=1/3x3/4=1/4

d: 4/9x12/16=48/144=1/3

e: 25/15x6/7=5/3x6/7=30/21=10/7

f: 6/10x15/20=90/200=9/20

Bài 1

4/5 x 6/7= 24/35

2/9 x 1/2= 2/18= 1/9

1/2 x 8/3= 8/6= 4/3

7/9 x 6/5= 42/45= 14/15

8/7 x 5/9= 40/63

10/11 x 22/15= 220/165= 4/3

Bài 2

2/6 x 5/3= 1/3 x 5/3=5/9

11/9 x 5/10= 11/9 x 1/2= 11/18

3/9 x 6/8= 1/3 x 3/4 =3/12= 1/4

4/9 x 12/16= 4/9 x 3/4= 12/36= 1/3

25/15 x 6/7= 5/3 x 6/7= 30/21= 10/7

6/10 x 15/20= 3/5 x 3/4= 9/20

bài 1

4/5 x 6/7 = 24/35

2/9 x 1/2 = 1/9

1/2 x 8/3 = 4/3

7/9 x 6/5 = 14/15

8/7 x 5/9 = 14/15

8/7 x 5/9 = 40/63

10/11 x 22/15 = 4/3

\(S=\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{29.32}\)

\(S=2.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{29}-\frac{1}{32}\right)\)

\(S=2.\left(\frac{1}{2}-\frac{1}{32}\right)\)

\(S=2.\frac{15}{31}\Rightarrow S=\frac{15}{16}< 1\)

\(S=\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{29.32}\)  

\(S=\left(\frac{1}{2}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{8}\right)+\left(\frac{1}{8}-\frac{1}{11}\right)+...+\left(\frac{1}{29}-\frac{1}{32}\right)\)

\(S=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{29}-\frac{1}{32}\)

\(S=\frac{1}{2}-\frac{1}{32}\)

\(S=\frac{17}{32}< 1\)

S=6/2.5+6/5.8+6/8.11+...+6/29.32
S=2.(1/2-1/5+1/5-1/8+1/8-1/11+...+1/29-1/32)
S=2.(1/2+1/32)
S=2.15/32
S=30/32=15/16
=>S<1

1: x=3/4-1/2=3/4-2/4=1/4

2: x-1/5=2/11

=>x=2/11+1/5=21/55

3: x-5/6=16/42-8/56

=>x-5/6=8/21-4/28=5/21

=>x=5/21+5/6=15/14

4: x/5=5/6-19/30

=>x/5=25/30-19/30=6/30=1/5

=>x=1

5: =>|x|=1/3+1/4=7/12

=>x=7/12 hoặc x=-7/12

6: x=-1/2+3/4

=>x=3/4-1/2=1/4

11: x-(-6/12)=9/48

=>x+1/2=3/16

=>x=3/16-1/2=-5/16

1)x= 1/4

2)x= 2/11+ 1/5

   x= 21/55

3)x - 5/6 = 5/21

   x         = 5/21+5/6

   x         = 15/14

4)x/5 = 5/6 + -19/30

   x:5 = 1/5

   x    = 1/5.5

   x    = 1

5) |x| - 1/4 = 6/18

    |x|           = 6/18 - 1/4

    |x|            =7/12

⇒x= 7/12 hoặc -7/12

6)x = -1/2 +3/4

   x= 1/4

7) x/15 = 3/5 + -2/3

   x:15  = -1/15

  x        = -1/15. 15

  x        = -1

8)11/8 + 13/6 = 85/x  

       85/24      = 85/x

  ⇒      x           = 24

9) x - 7/8 = 13/12

   x          = 13/12 + 7/8

   x          = 47/24

10)x - -6/15 = 4/27  

     x            = 4/27 + (-6/15)

    x             = -34/135

11) -(-6/12)+x = 9/48

                    x= 9/48 - 6/12

                    x = -5/16

12) x - 4/6 = 5/25 + -7/15

      x -4/6  =  -4/15

     x           = -4/15 + 4/6

    x             = 2/5

`Answer:`

Vì đề bài khá khó nhìn nên mình làm thành hai bài nhé. Đề nào đúng thì bạn tham khảo.

`x : (9 1/2 - 3/2 ) = 0,4 + 2/9 - 2/11 . 1/6 + 8/9 - 8/11`

`=> x : ( 19/2 - 3/2 ) = 28/45 - 1/33 + 8/9 - 8/11`

`=> x : 8 = 293/495 + 8/9 - 8/11`

`=> x : 8 = 733/495 - 8/11`

`=> x : 8 = 373/495`

`=> x = 373/495 .8`

`=> x = 2984/495`

`x : ( 9 1/2 - 3/2 ) = (0,4 + 2/9 - 2/11 )/(1,6 + 8/9 - 8/11 )`

`=> x : (19/2 - 3/2 ) = (2 . (1/5 + 1/9 - 1/11))/(8.(1/5 + 1/9 - 1/11))`

`=> x : 8 = 2/8`

`=> x = 2/8 .8`

`=> x = 2`

  Bài 1: 

1; ( - 35) : (-7) = 5

2; (- 42) : 21 =   - 2

3; 45 : (-9) = -5

4; 18 : 9 = 2

5; (- 30) : (- 15) = 2

6; 0 : 18 = 0

7; 0 : (-13) = 0

8; 44 : (-4) = - 11

9; - 55 : 11 = - 5

10; 46 : 23 = 2