18)Solve \(5x \equiv 4 \pmod{6}\)

18)Solve \(5x \equiv 4 \pmod{6}\)

Answer: \(5x \equiv 4 \pmod{6}\)

\(5x - 4 = 6k\) for some integer k.

\(x = \frac{6k+4}{5}\)

When we put k = 1, 6, 11, 16...

then \(6k + 4\) is divisible by 5.

If k=1, \(x = \frac{6(1)+4}{5} = \frac{10}{5} = 2\)

If k=6, \(x = \frac{6(6)+4}{5} = \frac{40}{5} = 8\)

If k=11, \(x = \frac{6(11)+4}{5} = \frac{70}{5} = 14\)

If k=16, \(x = \frac{6(16)+4}{5} = \frac{100}{5} = 20\)

Therefore, the solution are 2, 8, 14, 20,...