Solve the congruence, 3x-=2(mod4)

Answer 1

We attempt to isolate x in 3x ≡ 2(mod 4).

While we cannot attempt to divide both sides by 3, the right side can be rewritten to give

3x = 4x - x ≡ 2(mod 4).

Since 4x(mod 4) ≡ 0, we have

-x ≡ 2(mod 4)

We can now multiply both sides by -1 to get

x ≡ -2(mod 4)

Adding 4 to the right side to make it positive gives.

x ≡ 2(mod 4)

Finally, to get the general form, we can rewrite this as

x = 2 + 4n for some integer n.