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

=> 4(3x - y) = 3(x + y)

=> 12x - 4y = 3x + 3y

=> 9x = 7y

=> \(\frac{x}{y}=\frac{7}{9}\)

a) \(\frac{x+2}{-5}=\frac{2}{15}\)

=> \(\left(x+2\right).15=\left(-5\right).2=-10\)

=> \(x+1=\frac{-10}{15}=-\frac{2}{3}\)

=> \(x=-\frac{2}{3}-1=-\frac{5}{3}\)

b) \(\frac{x-1}{3}=\frac{2x+5}{5}\)

=> \(\left(x-1\right).5=\left(2x+5\right).3\)

=> \(5x-5=6x+15\)

=> \(-15-5=6x-5x\)

=> \(x=-20\)

c) \(\frac{-3}{3x-2}=\frac{4}{2x+1}\)

=> \(-3.\left(2x+1\right)=4.\left(3x-2\right)\)

=> \(-6x+\left(-3\right)=12x-8\)

=> \(-18x=-5\)

=> \(x=\frac{5}{18}\)

7 người bạn có số cái bắt tay là :

       7 x 6 : 2 = 21 ( cái )

6 người kia đã bắt tay số bạn là :

       1 + 2 + 3 + 4 + 5 + 6 = 21 ( bạn )

Bạn G bắt tay số bạn là : 

       21 - 21 = 0 ( bạn )

             Đáp số : 0 bạn

Đặt\(\frac{x}{4}=\frac{y}{7}=k\)\(\Rightarrow x=4k;y=7k\Rightarrow xy=4k.7k\)

                                                                  hay\(112=28k^2\)

                                                                   \(\Rightarrow k^2=4\)

                                                                   \(\Rightarrow k=2\)hoặc \(k=-2\)

+ ) Với k = 2 thì x = 8 và y = 14

+ ) Với x = - 2 thì x = - 8 : y = - 14

Vì x ; y cùng dấu nên ( x ; y ) = { ( 8 ;14 ) ; ( - 8 : -14 ) }

\(\frac{5x-2y}{3x+4y}=\frac{3}{4}\Rightarrow\left(5x-2y\right).4=\left(3x+4y\right).3\)

\(\Rightarrow20x-8y=9x+12y\)

\(\Rightarrow20x-9x=12y+8y\Rightarrow11x=20y\Rightarrow\frac{x}{y}=\frac{20}{11}\)

a. Theo t/c dãy tỉ số = nhau:

\(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{42}{7}=6\)

=>\(\frac{x}{2}=6\Rightarrow x=6.2=12\)

=>\(\frac{y}{5}=6\Rightarrow y=6.5=30\)

Vậy x=12; y=30.

b. \(\left|x-0,25\right|-\frac{5}{6}=1\frac{2}{3}\)

=> \(\left|x-0,25\right|=1\frac{2}{3}+\frac{5}{6}\)

=> \(\left|x-0,25\right|=\frac{5}{2}=2,5\)

+) x-0,25=2,5

=> x=2,5+0,25

=> x=2,75

+) x-0,25=-2,5

=> x=-2,5+0,25

=> x=-2,25

Vậy x \(\in\){-2,25; 2,75}.

c. y=kx

=> -17=k.8

=> k=-17/8

Vậy hệ số tỉ lệ là -17/8.

a) \(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{42}{7}=6\)

=> x=12   ;   y = 30

b)  \(\left|x-0,25\right|-\frac{5}{6}=1\frac{2}{3}=>\left|x-0,25\right|=\frac{5}{3}+\frac{5}{6}=\frac{5}{2}=2,5\)

=> x-0,25 = 2,5    hoac:  -2,5

=> x = 2,75      hoac x= -2,25

Vay: x la { 2,75  ;   -2,25 }

c) Ti le gi vay ban.

Neu thuan thi he so ti le la: \(-\frac{17}{8}\)

Neu nghich thi he so ti le la : -136

\(a,-0,52:x=-9,36:16,38\)

\(\Leftrightarrow\frac{-13}{25}:x=\frac{-4}{7}\)

\(\Leftrightarrow x=\frac{-13}{25}:\frac{-4}{7}\)

\(\Leftrightarrow x=\frac{91}{100}\)

\(b,\frac{x}{-15}=\frac{-60}{x}\)

\(\Leftrightarrow x^2=900\)

\(\Leftrightarrow x^2=\left(30,-30\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x=30\\x=-30\end{cases}}\)

\(c,\frac{-2}{x}=\frac{-x}{8}\)

\(\Leftrightarrow-\left(x^2\right)=-16\)

\(\Leftrightarrow x^2=16\)

\(\Leftrightarrow x^2=\left(4,-4\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}x=-4\\x=4\end{cases}}\)

\(d.3,8\div2x=\frac{1}{4}:2\frac{2}{3}\)

\(\Leftrightarrow3,8\div2x=\frac{3}{32}\)

\(\Leftrightarrow2x=3,8\div\frac{3}{32}\)

\(\Leftrightarrow2x=\frac{608}{15}\)

\(\Leftrightarrow x=\frac{608}{15}\div2\)

\(\Leftrightarrow x=\frac{304}{15}\)

\(e.0,25x\div3=\frac{5}{6}:0,125\)

\(\Leftrightarrow0,25x\div3=\frac{20}{3}\)

\(\Leftrightarrow0,25x=\frac{20}{3}.3\)

\(\Leftrightarrow\frac{1}{4}x=20\)

\(\Leftrightarrow x=20:\frac{1}{4}\)

\(\Leftrightarrow x=80\)

\(4\frac{1}{3}:\frac{x}{4}=\frac{6}{0,3}\)

\(\Rightarrow\frac{13}{3}:\frac{x}{4}=20\)

\(\Rightarrow\frac{x}{4}=\frac{13}{3}:20\)

\(\Rightarrow\frac{x}{4}=\frac{13}{60}\)

\(\Rightarrow x=\frac{13}{60}.4\)

\(\Rightarrow x=\frac{13}{15}\)

\(4\frac{1}{3}:\frac{x}{4}=\frac{6}{0.3}\)

\(\frac{13}{3}:\frac{x}{4}=20\)

\(\frac{x}{4}=\frac{13}{3}:20\)

\(\frac{x}{4}=\frac{13}{60}\)

\(x=\frac{13}{60}.4\)