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

Điều kiện: \(x \ne 0\)

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

Khi đó \(24.(1 + 2y) = 18.(1 + 4y)\)

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

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

\( \Rightarrow 24y = 6\)

\( \Rightarrow y = \dfrac{1}{4}\)

Với \(y = \dfrac{1}{4}\) thay vào \(\dfrac{{1 + 4y}}{{24}} = \dfrac{{1 + 6y}}{{6x}}\) ta được:

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

\( \Rightarrow \dfrac{2}{{24}} = \dfrac{{1 + \dfrac{3}{2}}}{{6x}}\) \( \Rightarrow \dfrac{1}{{12}} = \dfrac{{\dfrac{5}{2}}}{{6x}}\) \( \Rightarrow 6x = 12.\dfrac{5}{2}\) \( \Rightarrow 6x = 30\) \( \Rightarrow x = 5\)

Vậy \(x = 5\) (thỏa mãn).