Since $\gcd(48,81)>1,$ then $48x \equiv 30 \pmod{81}$ by $3$.
I get $16x \equiv 10 \pmod{27}.$ Then I do extended Euclidean algorithm and got $$27=1*16+11$$ $$16=1*11+5$$ $$11=2*5+1$$ $$5=5*1+0,$$ then $x=22$ but what would be the next step?
2026-04-05 01:16:02.1775351762
How to solve the modular equations using the extended Euclidean algorithm: $48x \equiv 30 \pmod{81}\,$?
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What you solved was the inverse of the coefficient $16\bmod 27$, which is indeed $22$. Now you have to multiply by the given constant $10$ on the right side of the equation, thus $22×10\equiv\color{blue}{4\bmod 27}$.