(This is assuming you know modular arithmetic already)
Looking at the first equation, x would have to be the values 2,7,12,17,22,27,...,etc. Looking at the second equation, x would have to be the values 1,8,15,22,29,...,etc. When you compare both sequences, you can see that 22 is the only value common in both of them. Therefore, the only value of x that satisfies both equations is 22.
