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Solution:

Let’s solve the inequality for x.

$\begin{array}{l}\Rightarrow x^2+10>110\\ \Rightarrow x^2>100\end{array}$

Using the patterns we observed earlier, since $x^2>100$, |x| > 10.

In other words, either $x>10\text{or}x<-10$. The only choice that works is -12 because -12 is less than -10. The choices 8 and -10 are neither greater than 10 nor less than -10.