\(\dfrac{1}{2}-\dfrac{1}{2}\left(3-2x\right)=0\)

\(\Rightarrow\dfrac{1}{2}\left[1-\left(3-2x\right)\right]=0\)

\(\Rightarrow\dfrac{1}{2}\left[1-3+2x\right]=0\)

\(\Rightarrow\dfrac{1}{2}\left[2x-2\right]=0\)

\(\Rightarrow2x-2=0\Rightarrow2x=2\Rightarrow x=1\)

x = 1 nha Nhật

a) \(\left(5x+3^4\right).6^8=6^9.3^4\)

\(=>6x+3^4=3^4.6^9:6^8\)

\(=>6x+3^4=3^4.6\)

\(=>6x=6.3^4-3^4\)

\(=>6x=0\)

\(=>x=0:6\)

\(=>x=0\)

a/(5x + 3⁴).6⁸=6⁹.3⁴

   (5x + 3⁴) = 6⁹:6⁸.3⁴

   5x + 81 = 6.81

   5x = 6.81 - 81

   5x = 486 - 81

   5x = 425

   x = 425:5

   x = 85

b/92 - 2x = 2.4²- 3.4 + 120:15
   92 - 2x = 2.16 - 12 + 8

   92 - 2x = 32 - 12 + 8

   92 - 2x = 28

   2x = 92 - 28

   2x = 64

   x = 64:2

   x = 32

c/5³.(3x + 2) : 13 = 10³: (13⁵:13⁴)

  125.(3x + 2) : 13 = 1000:13 

  125.(3x+2) = 1000:13.13

  125.(3x+2) = 1000

   3x + 2 = 1000:125

   3x + 2 = 8

   3x = 8 - 2

   3x = 6

   x = 6:3

   x = 2

Bạn nhớ tick cho mình nhé!

a/(5x + 34).68=69.34

   (5x + 34) = 69:68.34

   5x + 81 = 6.81

   5x = 6.81 - 81

   5x = 486 - 81

   5x = 405

   x = 405:5

   x = 81

b/92 - 2x = 2.42- 3.4 + 120:15
   92 - 2x = 2.16 - 12 + 8

   92 - 2x = 32 - 12 + 8

   92 - 2x = 28

   2x = 92 - 28

   2x = 64

   x = 64:2

   x = 32

c/53.(3x + 2) : 13 = 103: (135:134)

  125.(3x + 2) : 13 = 1000:13 

  125.(3x+2) = 1000:13.13

  125.(3x+2) = 1000

   3x + 2 = 1000:125

   3x + 2 = 8

   3x = 8 - 2

   3x = 6

   x = 6:3

   x = 2

Cái này mới đúng

Bạn nhớ tick cho mình nhé!

2.

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right).\left(2x+3\right)}=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{9}\right)+...+\frac{1}{2}.\left(\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{15}{93}:\frac{1}{2}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)

\(\Rightarrow\frac{1}{2x+3}=\frac{1}{93}\)

\(\Rightarrow\)2x + 3 = 93

\(\Rightarrow\)2x = 93 - 3

\(\Rightarrow\)2x = 90

\(\Rightarrow\)x = 90 : 2 = 45

\(H=\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{33.37}\)

= \(\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{33}-\frac{1}{37}\right)\)

= \(\frac{3}{4}\left(1-\frac{1}{37}\right)\)

= \(\frac{3}{4}.\frac{36}{37}=\frac{27}{37}\)

\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+...+\dfrac{4}{99.101}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=2\left(1-\dfrac{1}{101}\right)\)
\(=2\cdot\dfrac{100}{101}\)
\(=\dfrac{200}{101}\)

`c)4/1.3+4/3.5+4/5.7+...+4/99.101`

`=2(2/1.3+2/3.5+2/5.7+...+2/99.101)`

`=2(1/1-1/3+1/3-1/5+1/5-1/7+..+1/99-1/101)`

`=2(1/1-1/101)`

`=2(101/101-1/101)`

`=2 . 100/101`

`=200/101`

\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+...+\dfrac{4}{99.101}\\ =\dfrac{4}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\\ =2.\left(1-\dfrac{1}{101}\right)\\ =2.\dfrac{100}{101}\\ =\dfrac{200}{101}\)

Bài 3 : 

b) Ta có 1+ 2 + 3 +4 + ...+ x =15

Nên \(\frac{x\left(x+1\right)}{2}=15\)

\(x\left(x+1\right)=30\)

=> \(x\left(x+1\right)=5.6\)

=> x = 5

Bài 2:

h; \(\dfrac{2}{3}\)\(x\)  + 50% + \(x\) = \(\dfrac{1}{10}\)

    \(\dfrac{2}{3}\)\(x\) + \(\dfrac{1}{2}\)  + \(x\) = \(\dfrac{1}{10}\)

    (\(\dfrac{2}{3}\)\(x\) + \(x\)) + \(\dfrac{1}{2}\) = \(\dfrac{1}{10}\)

     \(x\) \(\times\) (\(\dfrac{2}{3}\) + 1) + \(\dfrac{1}{2}\) = \(\dfrac{1}{10}\)

      \(x\) \(\times\) \(\dfrac{5}{3}\) + \(\dfrac{1}{2}\) = \(\dfrac{1}{10}\)

      \(x\) \(\times\) \(\dfrac{5}{3}\) = \(\dfrac{1}{10}\) - \(\dfrac{1}{2}\)

      \(x\) \(\times\) \(\dfrac{5}{3}\) = \(\dfrac{-2}{5}\)

      \(x\)         = \(\dfrac{-2}{5}\): \(\dfrac{5}{3}\)

      \(x\)         =   - \(\dfrac{6}{25}\) 

Lớp 5 chưa học số âm em nhé. 

Bài 3:

a;  (\(x\) + 2) + (\(x\) + 4) + (\(x+6\)) + ... + (\(x+100\)) = 6000

     \(x\) + 2 + \(x\) + 4 + ... + \(x\) + 2 + 4 + 6 + ... + 100 = 6000

    (\(x\) + \(x\) + \(x\) + ... + \(x\)) + (2 + 4 + ... + 100) = 6000

     Xét dãy số 2; 4; ...;100;

Đây là dãy số cách đều với khoảng cách là: 4 - 2 = 2

Số số hạng của dãy số trên là: (100 - 2) : 2 + 1 = 50 (số)

 Theo bài ra ta có:

   \(x\) \(\times\) 50 + (100 + 2) \(\times\) 50 : 2 = 6000

   \(x\) \(\times\) 50 + 102 x 50 : 2 = 6000

    \(x\) \(\times\) 50 + (102 : 2) x 50 = 6000

    \(x\) x 50 + 51 x 50 = 6000

   \(x\) \(\times\) 50 + 2550 = 6000

    \(x\) x 50 = 6000 - 2550

    \(x\) x 50 = 3450

    \(x\) x 50 = 3450

   \(x\)           = 3450 : 50

   \(x\)           = 69

a) \(215+x=400\)

\(\Rightarrow x=400-215\)

\(\Rightarrow x=185\)

b) \(12,5-2x=\dfrac{1}{5}\)

\(\Rightarrow2x=12,5-\dfrac{1}{5}\)

\(\Rightarrow2x=\dfrac{123}{10}\)

\(\Rightarrow x=\dfrac{123}{10}:2\)

\(\Rightarrow x=\dfrac{123}{20}\)

còn câu c d nhanh cậu ơi

Bạn xem lại đề phần e nha .

\(c)x.0,25-\dfrac{3}{25}:x=2\dfrac{1}{4}\)

\(x.0,25-\dfrac{25}{3}.x=\dfrac{9}{4}\)

\(x.\left(0,25-\dfrac{25}{3}\right)=\dfrac{9}{4}\)

\(x.\dfrac{-97}{12}=\dfrac{9}{4}\)

\(x=\dfrac{-27}{97}\)

\(d)\left(x-\dfrac{1}{3}\right).\left(x-\dfrac{1}{4}\right)=0\)

Do : 2 số đó nhân với nhau bằng 0 nên một trong 2 số là số 0.

Do đó :

\(Th1:x-\dfrac{1}{3}=0\)

\(x=\dfrac{1}{3}\)

\(Th2:x-\dfrac{1}{4}=0\)

\(x=\dfrac{1}{4}\)

\(B=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+..+\frac{1}{55}\)

\(B=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)

\(B=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{10.11}\)

\(B=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(B=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)

làm cả 3 nhé 

bạn do not ask why làm sai ở bước 4 rồi