Simple Modulo Question $6x = 9 \pmod{11}$ I am trying to solve $6x = 9\pmod{11}$ 
The solution suggests notice that $2*6 = 12 = 1 \pmod {11}$
$$6x = 9 \pmod {11}\\12x = 18 \pmod {11}\\x = 7 \pmod{11}$$
I don't get the final step from $12x = 18\pmod{11}$ to the solution.

$6x \equiv 9 \pmod{11} \Rightarrow 2x\equiv 3 \pmod{11}  (\because (3,11)=1) \Rightarrow 2x\equiv 14 \pmod{11} (\because 14\equiv 3 \pmod{11}) \Rightarrow x\equiv 7 \pmod{11}.$  
