\(a.\)

\(-\dfrac{2}{3}\cdot\dfrac{?}{4}=\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{?}{4}=\dfrac{1}{2}:-\dfrac{2}{3}=\dfrac{1}{2}\cdot-\dfrac{3}{2}=-\dfrac{3}{4}\)

\(\Leftrightarrow?=-3\)

\(b.\)

\(\dfrac{?}{3}\cdot\dfrac{5}{8}=-\dfrac{5}{12}\)

\(\Leftrightarrow\dfrac{?}{3}=\dfrac{-5}{12}:\dfrac{5}{8}=\dfrac{-5}{12}\cdot\dfrac{8}{5}=-\dfrac{2}{3}\)

\(\Leftrightarrow?=-2\)

\(c.\)

\(\dfrac{5}{6}\cdot\dfrac{3}{?}=\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{3}{?}=\dfrac{1}{4}:\dfrac{5}{6}=\dfrac{1}{4}\cdot\dfrac{6}{5}=\dfrac{3}{10}\)

\(\Leftrightarrow?=10\)

Mk gọi ? = x nha

a) \(\dfrac{-2}{3}.\dfrac{x}{4}=\dfrac{1}{2}\) 

           \(\dfrac{x}{4}=\dfrac{1}{2}:\dfrac{-2}{3}\) 

           \(\dfrac{x}{4}=\dfrac{-3}{4}\) 

⇒x=-3

b)\(\dfrac{x}{3}.\dfrac{5}{8}=\dfrac{-5}{12}\)  

       \(\dfrac{x}{3}=\dfrac{-5}{12}:\dfrac{5}{8}\) 

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

⇒x=-2

c)\(\dfrac{5}{6}.\dfrac{3}{x}=\dfrac{1}{4}\) 

        \(\dfrac{3}{x}=\dfrac{1}{4}:\dfrac{5}{6}\) 

        \(\dfrac{3}{x}=\dfrac{3}{10}\) 

⇒x=10

Lời giải:

Ta có:

\(\text{VT}=\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.....\frac{30}{62}.\frac{31}{64}=\frac{1.2.3....31}{2.4.6.8...64}\)

Xét mẫu số:

\(2.4.6.8.....62.64=(2.1)(2.2)(2.3)(2.4)....(2.31)(2.32)\)

\(=2^{32}(1.2.3....31.32)\)

Suy ra:

\(\text{VT}=\frac{1.2.3....31}{2^{32}.(1.2.3...31.32)}=\frac{1}{2^{32}.32}=\frac{1}{2^{37}}\)

Do đó \(4^x=\frac{1}{2^{37}}\Leftrightarrow 2^{2x}=\frac{1}{2^{37}}\Leftrightarrow 2^{2x+37}=1\)

\(\Leftrightarrow 2x+37=0\Leftrightarrow x=-\frac{37}{2}\)

Vậy \(x=\frac{-37}{2}\)

\(a)\left(\dfrac{1}{2}+1,5\right)x=\dfrac{1}{5}\)

\(\Rightarrow2x=\dfrac{1}{5}\)

\(\Rightarrow x=\dfrac{1}{10}\)

\(b)\left(-1\dfrac{3}{5}+x\right):\dfrac{12}{13}=2\dfrac{1}{6}\)

\(\Leftrightarrow-\dfrac{8}{5}+x=\dfrac{13}{6}.\dfrac{12}{13}\)

\(\Leftrightarrow-\dfrac{8}{5}+x=2\)

\(\Leftrightarrow x=\dfrac{18}{5}\)

\(c)\left(x:2\dfrac{1}{3}\right).\dfrac{1}{7}=-\dfrac{3}{8}\)

\(\Leftrightarrow x:\dfrac{7}{3}=-\dfrac{3}{8}:\dfrac{1}{7}\)

\(\Leftrightarrow x=-\dfrac{21}{8}.\dfrac{7}{3}\)

\(\Leftrightarrow x=-\dfrac{49}{8}\)

\(d)-\dfrac{4}{7}x+\dfrac{7}{5}=\dfrac{1}{8}:\left(-1\dfrac{2}{3}\right)\)

\(\Leftrightarrow-\dfrac{4}{7}x+\dfrac{7}{5}=-\dfrac{3}{40}\)

\(\Leftrightarrow-\dfrac{4}{7}x=-\dfrac{59}{40}\)

\(\Leftrightarrow x=\dfrac{413}{160}\)

a= 1/10

b= 18/5

c= -49/8

d= 413

.

\(\Leftrightarrow2x-\dfrac{1}{3}=\left(\dfrac{12}{30}-\dfrac{4}{15}\right):\dfrac{3}{5}=\dfrac{2}{9}\)

=>2x=5/9

hay x=5/18

x= 5/18

\(\dfrac{3}{5}.\left(\dfrac{ }{ }2x-\dfrac{1}{3}\right)=\dfrac{12}{30}-\dfrac{4}{15}\)

\(\dfrac{3}{5}.\left(2x-\dfrac{1}{3}\right)=\dfrac{2}{15}\)

\(2x-\dfrac{1}{3}=\dfrac{2}{9}\)

2x= \(\dfrac{2}{9}+\dfrac{1}{3}\)

2x = \(\dfrac{5}{9}\)

x = \(\dfrac{5}{18}\)

a) \(\dfrac{4}{5}\left(x-\dfrac{1}{3}\right)-3\dfrac{1}{2}=50\%\)

\(\dfrac{4}{5}x-\dfrac{4}{15}-\dfrac{7}{2}=\dfrac{1}{2}\)

\(\dfrac{4}{5}x=\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{4}{15}\)

\(\dfrac{4}{5}x=\dfrac{64}{15}\)

\(x=\dfrac{64}{15}:\dfrac{4}{5}\\ x=\dfrac{16}{3}\)

b) \(8\dfrac{3}{5}.x-2\dfrac{1}{5}.x=16\%\)

\(\dfrac{43}{5}x-\dfrac{11}{5}x=\dfrac{4}{25}\)

\(\dfrac{32}{5}x=\dfrac{4}{25}\)

\(x=\dfrac{4}{25}:\dfrac{32}{5}\)

\(x=\dfrac{1}{40}\)

`3/5 : x =1/3 +1/2`

` 3/5 : x= 2/6 +3/6`

` 3/5 : x= 5/6`

` x= 3/5 : 5/6`

` x= 3/5 xx 6/5`

` x= 18/25`

__

`x: 7/15 =2`

` x= 2xx 7/15`

` x= 14/15`

__

`x-3/2=11/4-5/4`

`x-3/2= 6/4`

`x= 3/2 +3/2`

`x= 6/2`

`x=3`

__

`x+5/4 = 3/2+7/12`

`x+5/4 = 18/12+7/12`

`x+5/4 = 25/12`

`x= 25/12-5/4`

`x= 25/12- 15/12`

`x= 10/12`

`x= 5/6`

`#3107`

a)

\(\dfrac{11}{12}-\left(\dfrac{2}{5}+\dfrac{3}{4}x\right)=\dfrac{2}{3}?\\ \Rightarrow\dfrac{2}{5}+\dfrac{3}{4}x=\dfrac{11}{12}-\dfrac{2}{3}\\ \Rightarrow\dfrac{2}{5}+\dfrac{3}{4}x=\dfrac{1}{4}\\ \Rightarrow\dfrac{3}{4}x=\dfrac{1}{4}-\dfrac{2}{5}\\ \Rightarrow\dfrac{3}{4}x=-\dfrac{3}{20}\\ \Rightarrow x=-\dfrac{3}{20}\div\dfrac{3}{4}\\ \Rightarrow x=-\dfrac{1}{5}\)

Vậy, \(x=-\dfrac{1}{5}\)

b)

\(\dfrac{-2}{5}+\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=\dfrac{-7}{6}\\ \Rightarrow\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=\dfrac{-7}{6}-\dfrac{-2}{5}\\ \Rightarrow\dfrac{5}{3}\cdot\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=-\dfrac{23}{30}\\ \Rightarrow\dfrac{3}{2}-\dfrac{4}{15}x=-\dfrac{23}{30}\div\dfrac{5}{3}\\ \Rightarrow\dfrac{3}{2}-\dfrac{4}{15}x=-\dfrac{23}{50}\\ \Rightarrow\dfrac{4}{15}x=\dfrac{3}{2}-\left(-\dfrac{23}{50}\right)\\ \Rightarrow\dfrac{4}{15}x=\dfrac{49}{25}\\ \Rightarrow x=\dfrac{147}{20}\)

Vậy, \(x=\dfrac{147}{20}\)

c)

\(\dfrac{1}{2}+\dfrac{3}{4}x=\dfrac{1}{4}\\ \Rightarrow\dfrac{3}{4}x=\dfrac{1}{4}-\dfrac{1}{2}\\ \Rightarrow\dfrac{3}{4}x=-\dfrac{1}{4}\\ \Rightarrow x=-\dfrac{1}{4}\div\dfrac{3}{4}\\ \Rightarrow x=-\dfrac{1}{3}\)

Vậy, \(x=-\dfrac{1}{3}.\)

\(#Emyeu1aithatroi...\)

(2/5 + 3/4 . x)= 11/12 -2/3

(2/5 +3/4 . x)= 1/4

3/4 . x          = 1/4 - 2/5

3/4 . x          = -3/20

x                  = -3/20 : 3/4

x                  = -1/5

Vậy .....

`(2/3x-1/2)*3/4-2/5x=4 1/4`

`=>2/3x*3/4-1/2*3/4-2/5x=17/4`

`=>1/2x-3/8-2/5x=17/4`

`=>1/2x-2/5x=17/4+3/8`

`=>x(1/2-2/5)=37/8`

`=>x*1/10=37/8`

`=>x=37/8:1/10`

`=>x=37/8xx10`

`=>x=185/4`