How many values of $x$ satisfy both of the following conditions? (a) $x$ is a multiple of $7,$ not necessarily positive. (b) $x^2$ is less t

How many values of $x$ satisfy both of the following conditions?

$(a)$ $x$ is a multiple of $7,$ not necessarily positive.

$(b)$ $x^2$ is less than $500$.

If $x^2$ is $500,$ that means $-22\le x\le22$. Also, since $x$ is a multiple of $7,$ we can list all the multiples of 7 between -22 and 22 out.

-21, -14, -7, 0, 7, 14, 21

Therefore, since there are 7 terms in the list, the answer is $\boxed{7}$.