Show that a Language can be Generated by a regular grammar
The only thing that prevents your grammar from being a regular grammar is that $x$ is a string rather than a single terminal. That means that you have to deal with two kinds of problems:


$x$ is a string containing more than one terminal.
$x$ is the empty string.


To deal with the first problem, replace each problematic rule by a chain of equivalent rules of the proper form. For example, $A \to \alpha \beta$ is the same as $A \to \alpha X$ and $X \to \beta$.

To deal with the second problem, you have to get rid of rules of the form $A\to B$ and of rules of the form $A \to \epsilon$. Hopefully this is something you already know how to do. If not, notice that $A \to B$ means that whenever you have $A$, you can replace it with $B$, and $A \to \epsilon$ means that whenever you have $A$, you can remove it. Doing so recursively will allow you to get rid of these rules.