Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{1+2y+1+6y}{18+6x}=\frac{2+8y}{18+6x}\)

\(\Rightarrow\frac{1+4y}{24}=\frac{2+8y}{18+6x}\left(1\right)\)

Từ ( 1 )

=> \(\frac{1+4y}{2\left(1+4y\right)}=\frac{24}{18+6x}\)

\(=\frac{1}{2}=\frac{24}{18+6x}\)

\(\Rightarrow18+6x=48\)   

                   \(6x=48-18\)

                    \(6x=30\)

                       \(x=30:6\)   

                        \(x=5\)

Ta có : 

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có : 

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+2y+1+4y}{18+24}=\frac{2+6y}{42}=\frac{2\left(1+6y\right)}{2.21}=\frac{1+6y}{21}\)

Lại có : 

\(\frac{1+6y}{6x}=\frac{1+6y}{21}\)

\(\Leftrightarrow\)\(6x=21\)

\(\Leftrightarrow\)\(x=\frac{7}{2}\)

Vậy \(x=\frac{7}{2}\)

Chúc bạn học tốt ~ 

sai bạn phùng minh quân nhé

thử lại sẽ sai

nhưng mik sẽ k cho bạn vì đã cố gắng

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}\)

\(\Rightarrow\frac{1}{18}+\frac{2y}{18}=\frac{1}{24}+\frac{4y}{24}=\frac{1}{6x}+\frac{6y}{6x}\)

\(\Rightarrow\left(\frac{1}{18}+\frac{2y}{18}\right)-\left(\frac{1}{6x}+\frac{6y}{6x}\right)=0\)

\(\Rightarrow\frac{1}{18}+\frac{2y}{18}-\frac{1}{6x}-\frac{6y}{6x}=0\)

\(\frac{y}{9}-\frac{1}{6x}-\frac{6y}{6x}=\frac{1}{18}\)

\(\frac{\frac{2}{3}xy}{6x}-\frac{1}{6x}-\frac{6y}{6x}=\frac{1}{18}\)

\(\frac{\frac{2}{3}xy-1-6y}{6x}=\frac{1}{18}\)

\(6x=\left(\frac{2}{3}xy-1-6y\right)\cdot\frac{1}{18}\)

\(x=\frac{\left[\left(\frac{2}{3}xy-1-6y\right)\cdot\frac{1}{18}\right]}{6}\)

\(x=\left(\frac{\frac{\frac{2}{3}xy-1-6y}{18}}{6}\right)\)

\(x=\frac{\frac{2}{3}xy-1-6y}{108}\)

=5 đó pn ko chắc 100 phần trăm nha

ta có: \(\frac{1+2y}{18}=\frac{1+4y}{24}\)

\(\Rightarrow\left(1+2y\right).24=18.\left(1+4y\right)\)

\(24+48y=18+72y\)

\(48y-72y=18-24\)

\(-24y=-6\)

\(y=\frac{1}{4}\)

thay vào \(\frac{1+4.\frac{1}{4}}{24}=\frac{1+6.\frac{1}{4}}{6x}\)

\(\frac{1+1}{24}=\frac{1+\frac{3}{2}}{6x}\)

\(\frac{1}{12}=\frac{5}{2}:6x\)

\(6x=\frac{5}{2}:\frac{1}{12}\)

\(6x=30\)

\(x=30:6\)

\(x=5\)

KL: x =5; y = 1/4

\(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{1+2y+1+6y}{18+6x}=\frac{2+8y}{6\left(3+x\right)}=\frac{1+4y}{3\left(3+x\right)}\)

\(\Rightarrow3\left(3+x\right)=24\)\(\Rightarrow3+x=8\)\(\Rightarrow x=5\)

Vậy \(x=5\)

Ta có: \(\frac{1+2y}{18}=\frac{1+4y}{24}\)

\(\Leftrightarrow24\left(1+2y\right)=18\left(1+4y\right)\)

\(\Leftrightarrow24+48y=18+72y\)

\(\Leftrightarrow24y-6=0\Leftrightarrow y=\frac{1}{4}\)

\(\Rightarrow\frac{1+2y}{18}=\frac{1+6y}{6x}\Leftrightarrow\frac{1+\frac{1}{2}}{18}=\frac{1+\frac{3}{2}}{6x}\)

\(\Leftrightarrow x=5\)

Vậy x = 5 và \(y=\frac{1}{4}\)

1 + 2y/18=1 + 6y/6x=1 + 2y + 1 + 6y/18 + 6x=2 + 8y/18 + 6x=2.(1 + 4y)/2.(9 + 3x)=1 + 4y/9 + 3x

Suy ra:1 + 4y/9 + 3x=1 + 4y/24=>9 + 3x=24

3x=15

x=5

\(\Rightarrow\)\(\frac{1+2y+1+4y+1+6y}{18+24+6x}\)=\(\frac{\left(1+1+1\right)+2y+4y+6y}{6\left(3+4+x\right)}=\frac{y\left(2+4+6\right)+3}{6\left(3+4+x\right)}=\frac{3+y.12}{6\left(7+x\right)}\)

=\(\frac{3\left(1+4y\right)}{3.2\left(7+x\right)}=\frac{1+4y}{14+2x}\)

\(\Rightarrow\)\(\frac{1}{14}=\frac{2y}{x}\Rightarrow x=14.2y=28y\)

\(\frac{x}{y}=28\)

Ta có: \(\frac{1+2y}{18}=\frac{1+4y}{24}=\frac{1+6y}{6x}=\frac{1+2y+1+6y}{18+6x}=\frac{2\left(1+4y\right)}{6\left(x+3\right)}=\frac{1+4y}{3x+9}\)

\(=>\frac{1+4y}{24}=\frac{1+4y}{3x+9}\)\(=>3x+9=24\)

<=>3x=15

<=>x=5

Vậy x có giá trị bằng 5

Chúc bạn học tốt!