Lời giải:

\(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}=\frac{25-24}{24.25}+\frac{26-25}{25.26}+...+\frac{30-29}{29.30}\)

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

\(=\frac{1}{24}-\frac{1}{30}=\frac{1}{120}\)

Vậy:

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

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

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

\(x=-15\)

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

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

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

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

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

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

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

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

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

(1/24.25 + 1/25.26 + ... + 1/29.30) . 120 + x : 1/3 = -4

(1/24 - 1/25 + 1/25 - 1/26 + ... + 1/29 - 1/30) . 120 + x . 3 = -4

(1/24 - 1/30) . 120 + x . 3 = -4

(5/120 - 4/120) + x . 3 = -4

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

=> 1 + x . 3 = -4

=> x . 3 = -4 - 1

=> x . 3 = -5

=> x = -5/3

Vậy x = -5/3

{1\24.25 + 1\25.26 +...+ 1\29.30} .120+x:1\3 = -4

\(120\left(\dfrac{1}{24.25}+\dfrac{1}{25.26}+...+\dfrac{1}{29.30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}+\dfrac{1}{26}+...+\dfrac{1}{29}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120.\dfrac{1}{120}+x=\dfrac{1}{3}\)

\(\Rightarrow1+x=\dfrac{1}{3}\)

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

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

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

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

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

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

\(\Rightarrow x=4\)

=> 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

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

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

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

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

=(1/24-1/25+1/25-1/24+...+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=-4-1/120

x:1/3=-481/120

x=-481/120.1/3

x=-481/360

số to lắm bạn nhé!

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

Ta có: \(\frac{1}{24.25}+\frac{1}{25.26}+...+\frac{1}{29.30}\)

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

\(=\frac{1}{24}-\frac{1}{30}\)

\(=\frac{1}{120}\)

Thay vào ta có: \(\frac{1}{120}.120+y:\frac{1}{3}=-4\)

\(\implies 1+y:\frac{1}{3}=-4\)

\(\implies y:\frac{1}{3}=-5\)

\(\implies y=-5.\frac{1}{3}\)

\(\implies y=\frac{-5}{3}\). Vậy \(y=\frac{-5}{3}\)

~ Học tốt a~

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

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

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

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

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

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

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

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

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

Vậy  \(y=\frac{-5}{3}\)

_Chúc bạn học tốt_