Question

solve the congruence 5x=2(mod26)

Answer 1

$x\equiv\frac{2}{5}\equiv\frac{2\times{5}}{5\times{5}}\equiv\frac{10}{25}\equiv\frac{10}{-1}\equiv-10\equiv{16}\pmod{26}$

Answer 2

as 5x is congruent to 2 modulo 16, 5x-2 is divisible by 26 . that means, let x be -5 then 5x-2 = -26 
as -26 is divisible by 26, x=-5 .