More Adventures with Modular Arithmetic

If $4x \equiv 1 \text{ mod } 7$, one possible value of $x$ is $2$ (since $4 \times 2 = 8 \equiv 1 \text{ mod }7$).  

Find the value of $4x \text{ mod }7$ when $x = 9, 16, 23, ...$ 

Can you use this to help you find a general form for $x$?