\(\Rightarrow\frac{x}{1}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=\frac{6x+7y+8z}{6.4+7.12+8.15}=\frac{456}{228}=2\)

=> x= 4.2 =8

y = 12.2 =24

z = 15.2 =30

3x=y

=>x/1=y/3

=>x/4=y/12

5y=4z

=>y/4=z/5

=>y/12=z/15

=>x/4=y/12=z/15

=>6x/24=7y/84=8z/120

áp dụng tc dãy ts = nhau ta có :

6x/24=7y/84=8z/120 = 6x+7y+8z/24+84+120=456/228=2

=>x/4=2=>x=8

=>y/12=2=>y=24

=>z/15=2=>z=30

vậy ...

3x=y nên x=y/3 nên x/4=y/12

5y=4z nên y/4=z/5  nên y/12=z/15

=>x/4=y/12=z/15

nên 6x/24=7y/84=8z/120

Áp dụng tính chất dãy tỉ số bằng nhau, ta được:

 6x/24=7y/84=8z/120=(6x+7y+8z)/(24+84+120)=456/228=2

Do đó, x/4=2 nên x=2*4=8

          y/12=2 nên y=2*12=24

          z/15=2 nên z=2*15=30

Giải:

Ta có: \(3x=y\Rightarrow\frac{x}{1}=\frac{y}{3}\Rightarrow\frac{x}{4}=\frac{y}{12}\)

\(5y=4z\Rightarrow\frac{y}{4}=\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{15}\)

\(\Rightarrow\frac{x}{4}=\frac{y}{12}=\frac{z}{15}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=\frac{6x}{24}=\frac{7y}{84}=\frac{8z}{120}=\frac{6x+7y+8z}{24+84+120}=\frac{456}{228}=2\)

+) \(\frac{x}{4}=2\Rightarrow x=8\)

+) \(\frac{y}{12}=2\Rightarrow y=24\)

+) \(\frac{z}{15}=2\Rightarrow z=30\)

Vậy bộ số \(\left(x;y;z\right)\) là \(\left(8;24;30\right)\)

Ta có: 3x =y

\(\Rightarrow\frac{x}{1}=\frac{y}{3}\) \(\Rightarrow\frac{x}{4}=\frac{y}{12}\) (1)

5y = 4z

\(\Rightarrow\frac{y}{4}=\frac{z}{5}\\ \Rightarrow\frac{y}{12}=\frac{z}{15}\) (2)

Từ (1),(2) ta \(\Rightarrow\) \(\frac{x}{4}=\frac{y}{12}=\frac{z}{15}\) Do đó ta có : \(\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=\frac{6x}{24}=\frac{7y}{84}=\frac{8z}{120}=\frac{6x+7y+8z}{24+84+120}=\frac{456}{228}=2\)

Từ đó\(\Rightarrow\) x =2*4=8

y=2*12=21

z=2*15=30

Vậy:(x;y;z) là (8;21;30)

Chúc bạn học tốt.

\(\hept{\begin{cases}3x=y\\5y=4z\end{cases}\Rightarrow\hept{\begin{cases}\frac{3x}{12}=\frac{y}{12}\\\frac{5y}{60}=\frac{4z}{60}\end{cases}\Rightarrow}\hept{\begin{cases}\frac{x}{4}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{15}\end{cases}\Rightarrow}\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=\frac{6x}{24}=\frac{7y}{84}=\frac{8z}{120}=\frac{6x+7y+8z}{24+84+120}=\frac{456}{228}=2\Rightarrow x=2.4=8}\)

+ \(3x=y\Rightarrow6x=2y\)

+ \(4z=5y\Rightarrow8z=10y\)

Thay vào biểu thức

\(6x+7y+8z=2y+7y+10y=456\)

\(\Rightarrow19y=456\Rightarrow y=24\)

Từ đó suy ra x và z

a: \(\Leftrightarrow-15x+10=-7x+14\)

=>-8x=4

hay x=-1/2

\(a,\dfrac{2-3x}{x-2}=-\dfrac{7}{5}\left(x\ne2\right)\\ \Leftrightarrow14-7x=10-15x\\ \Leftrightarrow8x=-4\Leftrightarrow x=-2\left(tm\right)\\ c,\Leftrightarrow\dfrac{x-1}{2}=\dfrac{y-2}{5}=\dfrac{z-3}{4}=\dfrac{2x-2+3y-6-z+3}{2\cdot2+5\cdot3-4}=\dfrac{45}{15}=3\\ \Leftrightarrow\left\{{}\begin{matrix}x-1=6\\y-2=15\\z-3=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=17\\z=15\end{matrix}\right.\\ d,\Leftrightarrow\dfrac{x}{1}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\\ \Leftrightarrow\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{6x+7y+8z}{24+84+120}=\dfrac{456}{228}=2\\ \Leftrightarrow\left\{{}\begin{matrix}x=8\\y=24\\z=30\end{matrix}\right.\)

\(\frac{x}{1}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\Leftrightarrow\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=\frac{6x+7y+8z}{6.4+7.12+8.15}=\frac{456}{228}=2\)

x=4.2=8

y=12.2=24

z=15.2=30

\(3x=y\)=> \(x=\frac{y}{3}\)=> \(\frac{x}{4}=\frac{y}{12}\)

\(5y=4z\)=> \(\frac{y}{4}=\frac{z}{5}\)=> \(\frac{y}{12}=\frac{z}{15}\)

=> \(\frac{x}{4}=\frac{y}{12}=\frac{z}{15}\)

=> \(\frac{6x}{24}=\frac{7y}{84}=\frac{8z}{120}=\frac{6x+7y+8z}{24+84+120}=\frac{456}{228}=2\)

<=> \(\frac{x}{4}=\frac{y}{12}=\frac{z}{15}=2\)

=> x = 2 . 4 = 8

y = 2 . 12 = 24

z = 2 . 15 = 30

KL: ........