+5 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 $500$.
+166 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 \(\boxed{7}\).
