How to combine OR linear inequality with absolute value

Question

I have x < -10 OR x > 15

How do I turn it into a single inequality using an absolute value? Like a < |x+b|. What are the rules? I'm not sure if it is right, but I'm expecting an answer something like how factoring quadratic trinomials would be explained, which is really straightforward.

Thank you

Answer 1

Hint: You can use the distance from midpoint argument, or use quadratics:$$x < -10 \text{ OR } x> 15 \iff (x+10)(15-x) < 0 \\ \iff (x-\tfrac52)^2> \tfrac{625}4 \iff |x - \tfrac52| > \tfrac{25}2$$