Question

Solve the inequality x^2<16

Answer 1

The above answer is false.
If you were to solve this problem as if it were an equal sign, you would normally square root both sides and get an answer of x = +/- 4. In this case, though, we will do the same thing, but consider something slightly different. If \(x^{2} < 16\), then we have:
\(\sqrt{x^{2}} < \sqrt{16}\)
\(|x| < 4\)

Here we introduce the concept that \(\sqrt{x^2}\) = |x|. Without knowing this, square rooting both sides gives us something silly. So, that being said, we now have the ineqaulity |x| < 4. When you have an absolutely value inequality in the form |x| < a, this is equivalent to saying -a < x < a. GIven that, |x| < 4 is equaivalent to -4 < x < 4.
What I did may seem a little odd, so ask me if something doesnt make sense and I can try and reexplain or we can take a different approach to solving this :)

Answer 2

Just to clarify, after all that the answer is -4 < x < 4. I didnt want that to get lost in what I said, lol.

Answer 3

Thank you!

Answer 4

Great job @Concentrationalizing! I misread the equation as x^2 = 16 not x^2 < 16. Thank you for correcting me! :)