$y \equiv 7x\pmod{26}$ to encrypt the plaintext message “WATCH OUT”.
$A=0$
$Z=25$
I would assume that I would need to solve the $y\equiv 7x \pmod{26}$ equation firstly, before I would then be able to encrypt the "watch out" material. At present, I am not sure how to do this.
If the clear-text digit is $x$ and the encrypted digit is $y\equiv 7x\mod{26}$, then for example $E=4$ maps to $y = 7\cdot 4 = 28\equiv 2\mod{26}$, so the encrypted value is C.
If you mean for the clear-text value to be $y$ and the encrypted value for $x$, then you must first solve $y\equiv 7x\mod{26}$ for $x$: $x = 7^{-1}\cdot y\mod{26}$, and now you must find the multiplicative inverse of $7$ modulo $26$.