Question

Tìm x, biết rằng : \(\dfrac{1+2x}{18}=\dfrac{1+4y}{24}=\dfrac{1+6y}{6x}\)

giúp mik vs

Answer 1

Sửa đề:

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

Giải:

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

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

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

\(\Leftrightarrow48y-72y=18-24.\)

\(\Leftrightarrow-24y=-6.\)

\(\Leftrightarrow y=\dfrac{-6}{-24}=\dfrac{1}{4}.\)

Thay \(y=\dfrac{1}{4}\) vào \(\dfrac{1+4y}{24}=\dfrac{1+6y}{6x}\), ta có:

\(\dfrac{1+4.\dfrac{1}{4}}{24}=\dfrac{1+6.\dfrac{1}{4}}{6x}.\)

\(\Rightarrow\dfrac{1+1}{24}=\dfrac{1+\dfrac{3}{2}}{6x}.\)

\(\Rightarrow\dfrac{2}{24}=\dfrac{2,5}{6x}.\)

\(\Rightarrow6x=\dfrac{24.2,5}{2}.\)

\(\Rightarrow6x=30.\)

\(\Rightarrow x=\dfrac{30}{6}=5.\)

Vậy \(x=5.\)