If two fractions are equal to each other, then their inverses must be equal as well:
[tex] \dfrac{a}{b} = \dfrac{c}{d} \implies \dfrac{b}{a} = \dfrac{d}{c} [/tex]
So, we have
[tex] \dfrac{1}{54x} = \dfrac{1}{9} \implies 54x = 9 [/tex]
Now divide both sides by 54:
[tex] x = \dfrac{9}{54} = \dfrac{1}{6} [/tex]
Note:
Given the slightly ambiguous way the question is written, you may also mean
[tex] \dfrac{1}{54}\; x = \dfrac{1}{9} [/tex]
In this case, simply multiply both sides by 54:
[tex] x = \dfrac{54}{9} = 6 [/tex]
