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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 $500$.

 Aug 23, 2022
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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 \(\boxed{7}\).

 Aug 24, 2022

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