[Tex/LaTex] Proper punctuation after cases environment

casesmath-modepunctuationtypography

I know that when writing a displayed equation, it's correct to write punctuation before the closing \] as follows:

This proves $x^2 = 3,$ and it follows that $x = \pm\sqrt{3}.$


If I'm using a cases environment, where's the correct place for the period to end the sentence?

Absolute value is defined as $\lvert x \rvert = \begin{cases} x & \text{if x \ge 0} \\ -x & \text{if x < 0} \end{cases}$


If I put it after the cases environment, it looks funny. If I leave it off completely, then it also looks bad. It looks okay to put it at the end of the second line ($x < 0$.}), but are there any better solutions?