Dear Uncle Colin,
I’m pretty good with quadratic inequalities and pretty good with absolute values, but when I get the two together, I get confused. For example, I struggled with the set of values satisfying $x^2 -\left| 5x-3\right| < 2 + x$. Can you help?
– Nasty Absolute Value Inequalities Ending Rongly
Hi, NAVIER, and thanks for your message!
These are nasty, but can be made simpler by rearranging and sketching.
I would begin by getting the absolute value on one side and everything else on the other: $ x^2 – x – 2 < \left| 5x-3\right|$.
The left-hand side is a quadratic…
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