You did a great job. Think of radius as the maximum distance away from x. To help see this consider the following calculations.

First of all the ratio test gives us,

So you can see x can move 1/3 units in either direction from -4.

An alternate way of seeing this is from the ratio test you have

(this is the way you'd do it on a test {quicker}).

If you cannot see it by this form, then let's go one more step