4x = 5 (mod 9) { Pardon me for writing = as the equivalent sign }
Now as we know that : ax = b( mod ) is the form equation and we have the ( a,b ) are relative co prime to each other .
4x = 5(mod 9 ) ---→ This mean that both side should leave the remainder same .
and we now that : -4 = 5(mod 9 ) , bcz -4 = 9 * (-1) + 5 { as 5 as the remainder when -4 divided by 9}
so now eqn is : 4x = –4 (mod 9 )
Now ,
4*x = 4 *(-1) (mod 9)
Now we have common number both side as 4 to divide we follow : ac = bc (mod n )
a = b ( mod n /gcd(c,n))
x = -1 (mod 9)
now -1 = 8 (mod 9 ) so they are equivalent to each other )
Option b seems to be correct .