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11 tháng 7 2018

\(\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+y:\frac{1}{3}=-4\)

\(\Leftrightarrow\)\(\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+y:\frac{1}{3}=-4\)

\(\Leftrightarrow\)\(\left(\frac{1}{24}-\frac{1}{30}\right).120+y:\frac{1}{3}=-4\)

\(\Leftrightarrow\)\(1+3y=-4\)

\(\Leftrightarrow\)\(3y=-5\)

\(\Leftrightarrow\)\(y=-\frac{5}{3}\)

Vậy...

11 tháng 7 2018

Ta có : 

\(\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+y:\frac{1}{3}=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+y.3=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{30}\right).120+y.3=-4\)

\(\Rightarrow\left(\frac{5}{120}-\frac{4}{120}\right).120+y.3=-4\)

\(\Rightarrow\frac{1}{120}.120+y.3=-4\)

\(\Rightarrow1+y.3=-4\)

\(\Rightarrow3y=-4-1\)

\(\Rightarrow3y=-5\)

\(\Rightarrow y=-\frac{5}{3}\)

Vậy \(y=-\frac{5}{3}\)

a)\(\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+x:\frac{1}{3}=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+x:\frac{1}{3}=-4\)

\(\Rightarrow\left(\frac{1}{24}-\frac{1}{30}\right).120+x:\frac{1}{3}=-4\)

\(\Rightarrow\frac{1}{120}.120+x:\frac{1}{3}=-4\)

\(\Rightarrow1+x:\frac{1}{3}=-4\)

\(\Rightarrow x:\frac{1}{3}=-4-1=-5\)

\(\Rightarrow x=-5.\frac{1}{3}=\frac{-5}{3}\)

b)\(1\frac{3}{5}+\left(\frac{\frac{2}{7}+\frac{2}{17}+\frac{2}{37}}{\frac{5}{7}+\frac{5}{17}+\frac{5}{37}}\right).x=\frac{16}{5}\)

\(\Rightarrow\frac{8}{5}+\left[\frac{2.\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{37}\right)}{5.\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{37}\right)}\right].x=\frac{16}{5}\)

\(\Rightarrow\frac{8}{5}+\frac{2}{5}.x=\frac{16}{5}\)

\(\Rightarrow\frac{2}{5}.x=\frac{16}{5}-\frac{8}{5}=\frac{8}{5}\)

\(\Rightarrow x=\frac{8}{5}:\frac{2}{5}=\frac{8}{5}.\frac{5}{2}=\frac{8}{2}=4\)

\(\Rightarrow x=4\)

13 tháng 4 2016

y=-5/3 

13 tháng 4 2016

y=-5/3

17 tháng 4 2018

=> 1/24 - 1/25 + 1/25 - 1/ 26 + .... + 1/29 - 1/30 + x : 1/3 = -4

=> 1/24 - 1/30 + x : 1/3 = - 4

=> 1/ 120 + x : 1/3 = -4

=> x : 1/3 = 481/120

=> x = 481/360 

Vậy x = 481/360

17 tháng 4 2018

\(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}+x:\frac{1}{3}=-4\)

\(\Rightarrow\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}+x\times3=-4\)

\(\Rightarrow\frac{1}{24}-\frac{1}{30}+3x=-4\)

\(\Rightarrow\frac{1}{120}+3x=-4\)

22 tháng 6 2018

 Câu a) :

x=-5/3

Câu b) :

GỢI Ý : 3n-5 phải chia hết cho n-4 để A là số nguyên ( đk : n khác 4)

30 tháng 7 2018

\(a,\left(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\right).120+x:\frac{1}{3}=-4\)

\(\left(\frac{1}{24}-\frac{1}{25}+\frac{1}{25}-\frac{1}{26}+...+\frac{1}{29}-\frac{1}{30}\right).120+3x=-4\)

\(\left(\frac{1}{24}-\frac{1}{30}\right).120+3x=-4\)

\(\frac{1}{120}.120+3x=-4\)

\(1+3x=-4\)

\(\Rightarrow3x=-5\)

\(\Rightarrow x=-\frac{5}{3}\)

\(b,A=\frac{3n-5}{n-4}=\frac{3n-12+7}{n-4}=3+\frac{7}{n-4}\)

Để \(A\in Z\Rightarrow7⋮n-4\Leftrightarrow n-4\in\left(1;-1;7;-7\right)\)

\(\Rightarrow n\in\left(5;3;11;-3\right)\)

28 tháng 7 2018

a)  \(\left|x+\frac{1}{2}\right|=\frac{1}{3}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x+\frac{1}{2}=\frac{1}{3}\\x+\frac{1}{2}=-\frac{1}{3}\end{cases}}\) \(\Leftrightarrow\)\(\orbr{\begin{cases}x=-\frac{1}{6}\\x=-\frac{5}{6}\end{cases}}\)

Vậy....

b)  \(\left|x-\frac{1}{2}\right|=\frac{1}{3}-\frac{1}{2}\)

\(\Leftrightarrow\)\(\left|x-\frac{1}{2}\right|=-\frac{1}{6}\)   vô lí do \(\left|a\right|\ge0\)

Vậy pt vô nghiệm

c)  \(\left|x+\frac{1}{3}\right|-4=-1\)

\(\Leftrightarrow\)\(\left|x+\frac{1}{3}\right|=3\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x+\frac{1}{3}=3\\x+\frac{1}{3}=-3\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{8}{3}\\x=-\frac{10}{3}\end{cases}}\)

Vậy..

28 tháng 7 2018

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

\(\Leftrightarrow\)\(\left|x-\frac{1}{5}\right|+\frac{1}{3}=-\frac{5}{4}\)

\(\Leftrightarrow\)\(\left|x-\frac{1}{5}\right|=-\frac{19}{12}\)vô lí do  \(\left|a\right|\ge0\)với mọi a

Vậy pt vô nghiệm

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

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

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-\frac{5}{2}=\frac{7}{6}\\x-\frac{5}{2}=-\frac{7}{6}\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=3\frac{2}{3}\\x=\frac{4}{3}\end{cases}}\)

Vậy...