\(\left(y+1\right)+\left(y+4\right)+\left(y+7\right)+....+\left(y+31\right)=231\)

\(\Rightarrow\left(y+y+...+y\right)+\left(1+4+7+...+31\right)=231\)

\(\Rightarrow11y+176=231\)

\(\Rightarrow11y=231-176\)

\(\Rightarrow11y=55\)

\(\Rightarrow y=55:11\)

\(\Rightarrow y=5\)

Vậy y = 5

(y+1)+(y+4)+(y+7)+..........+(y+31)=231

y+1+y+4+y+7+y+10+..........+y+31=231

(y+y+y+y+........+y+y)+(1+4+7+10+....+31)=231

y*11+176=231

y*11=231-176

y*11=55

y=55 :11

y=5

vậy y=5

a) pt <=> (2x-1)(2y+3)=7

TH1: 2x-1=7 và 2y+3=1

<=> x = 4 và y = -1

TH2: 2x - 1 = -7 và 2y + 3 = -1

<=> x = -3 và y = -2

TH3: 2x-1=1 và 2y+3=7

<=> x = 1 và y=2

TH4: 2x-1=-1 và 2y+3=-7

<=> x=0 và y=-5

b) pt <=> (x-3)(y+4)=19

TH1: x - 3=1 và y+4=19

<=> x=4 và y=15

TH2: x-3=-1 và y+4=-19

<=> x=2 và y=-23

TH3: x-3=19 và y+4=1

<=> x=22 và y=-3

TH4: x-3=-19 và y+4=-1

<=> x=-16 và y=-5

(y + 1) + (y + 4) + ... + (y + 31) = 231

( y + y + ... + y ) + ( 1 + 4 + ... + 31 ) = 231

Số số hạng là : ( 31 - 1 ) : 3 + 1 = 11 ( số )

Tổng là : ( 31 + 1 ) . 11 : 2 = 176

=> 11y + 176 = 231

=> 11y = 55

=> y = 5

Vậy..........

Ta có \(\left(y+1\right)+\left(y+4\right)+\left(y+7\right)+\left(y+10\right)+...+\left(y+31\right)=231\)

\(\Rightarrow\left(y+y+y+...+y\right)+\left(1+4+7+10+....+31\right)=231\)

\(\Rightarrow10y+\frac{\left(31+1\right).10}{2}=231\)

\(\Rightarrow10y+160=231\)

\(\Rightarrow10y=71\)

\(\Rightarrow y=7,1\)

Vậy y = 7.1

a, y \(\times\) \(\dfrac{4}{3}\) = \(\dfrac{16}{9}\)

    y         =    \(\dfrac{16}{9}\) : \(\dfrac{4}{3}\)

    y         = \(\dfrac{4}{3}\)

b, ( y - \(\dfrac{1}{2}\)) + 0,5 = \(\dfrac{3}{4}\)

    y - 0,5 + 0,5 = \(\dfrac{3}{4}\)

   y                   = \(\dfrac{3}{4}\)

c, \(\dfrac{4}{5}-\dfrac{2}{5}y\) = 0,2

   0,8 - 0,4y = 0,2

           0,4y = 0,8 - 0,2

           0,4y  = 0,6

               y = 1,5

d, (y + \(\dfrac{3}{4}\)) \(\times\) \(\dfrac{5}{7}\) = \(\dfrac{10}{9}\)

    y + \(\dfrac{3}{4}\)           = \(\dfrac{10}{9}\) : \(\dfrac{5}{7}\)

   y + \(\dfrac{3}{4}\)            = \(\dfrac{14}{9}\)

y                    = \(\dfrac{14}{9}\) - \(\dfrac{3}{4}\)

 y                   =   \(\dfrac{29}{36}\)

e, y : \(\dfrac{5}{4}\)         = \(\dfrac{9}{5}\)  + \(\dfrac{1}{2}\)

   y : \(\dfrac{5}{4}\)         =   \(\dfrac{23}{10}\)

  y                =      \(\dfrac{23}{10}\)

  y               =   \(\dfrac{23}{8}\)

f, y \(\times\) \(\dfrac{1}{2}\) + \(\dfrac{3}{2}\) \(\times\) y   = \(\dfrac{4}{5}\)

   y \(\times\) ( \(\dfrac{1}{2}+\dfrac{3}{2}\))      =  \(\dfrac{4}{5}\)

   2y                       = \(\dfrac{4}{5}\)

    y                        = \(\dfrac{2}{5}\)

a) \(\frac{7}{10}-y\cdot\frac{3}{4}=\frac{1}{5}\)

\(y\cdot\frac{3}{4}=\frac{7}{10}-\frac{1}{5}\)

\(y\cdot\frac{3}{4}=\frac{1}{2}\)

\(y=\frac{1}{2}:\frac{3}{4}\)

\(y=\frac{1}{2}\cdot\frac{4}{3}\)

\(y=\frac{2}{3}\)

b) \(\frac{5}{6}:\left(y+\frac{7}{9}\right)=\frac{3}{4}\)

\(y+\frac{7}{9}=\frac{5}{6}:\frac{3}{4}\)

\(y+\frac{7}{9}=\frac{5}{6}\cdot\frac{4}{3}\)

\(y+\frac{7}{9}=\frac{10}{9}\)

\(y=\frac{10}{9}-\frac{7}{9}\)

\(y=\frac{3}{9}=\frac{1}{3}\)

**** !

a, \(\frac{7}{10}-y\times\frac{3}{4}=\frac{1}{5}\)

\(\Rightarrow y\times\frac{3}{4}=\frac{7}{10}-\frac{1}{5}\)

\(\Rightarrow y\times\frac{3}{4}=\frac{1}{2}\)

\(\Rightarrow y=\frac{1}{2}\div\frac{3}{4}\)

\(\Rightarrow y=\frac{1}{3}\)

b, \(\frac{5}{6}\div\left(y+\frac{7}{9}\right)=\frac{3}{4}\)

\(\Rightarrow y+\frac{7}{9}=\frac{5}{6}\div\frac{3}{4}\)

\(\Rightarrow y+\frac{7}{9}=\frac{10}{9}\)

\(\Rightarrow y=\frac{10}{9}-\frac{7}{9}\)

\(\Rightarrow y=\frac{1}{3}\)

Bài 5 :

a) \(\dfrac{y}{4}=\dfrac{9}{y}\)

\(\Rightarrow y^2=36\left(y\ne0\right)\)

\(\Rightarrow y=\pm6\)

b) \(\dfrac{y+7}{20}=\dfrac{5}{y+7}\left(y\ne-7\right)\)

\(\Rightarrow\left(y+7\right)^2=100=10^2\)

\(\Rightarrow\left[{}\begin{matrix}y+7=10\\y+7=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}y=3\\y=-17\end{matrix}\right.\)

c) \(\dfrac{4-5y}{3}=\dfrac{y+2}{5}\)

\(\Rightarrow5\left(4-5y\right)=3\left(y+2\right)\)

\(\Rightarrow20-25y=3y+6\)

\(\Rightarrow28y=14\)

\(\Rightarrow y=\dfrac{14}{28}=\dfrac{1}{2}\)

Bài 4 :

\(\dfrac{a}{5}=\dfrac{b}{7}=\dfrac{c}{10}\)

\(\Rightarrow\dfrac{2a}{10}=\dfrac{3b}{21}=\dfrac{4c}{40}=\dfrac{2a+3b-4c}{10+21-40}=\dfrac{81}{-9}=-9\)

\(\Rightarrow\left\{{}\begin{matrix}a=-9.5=-45\\b=-9.7=-63\\c=-9.10=-90\end{matrix}\right.\)