- #1
flyingpig
- 2,579
- 1
Homework Statement
Very embarrassing that I had problems with this. I managed to solved it at the end, but I am posting this for two reasons
1) I like someone else to work it out in a different method, I wnt to see what other approaches there are
2) Whether mine is taking too long or not. I mean I solved it, but any unnecessary steps?
3) Check whether I am right or wrong lol
[tex]|x^2 + 6x + 16| < 8[/tex]
The Attempt at a Solution
At first I was going to do
[tex] - 8 < x^2 + 6x + 16 < 8[/tex]
Then I realize it was hopeless
So then I did
[tex] (x^2 + 6x + 16) < 8[/tex] and [tex] - ( x^2 + 6x + 16 ) < 8[/tex](1) [tex] (x^2 + 6x + 16) < 8[/tex][tex] x^2 + 6x + 8 < 0[/tex][tex] (x+4)(x+2) < 0[/tex]
Did some test points and found that [tex] x \in (-4,-2) [/tex] is a solution
(2) [tex] -(x^2 + 6x + 16) < 8[/tex]
[tex] -(x+4)(x+2) < 0[/tex]
[tex](x+4)(x+2) > 0[/tex]
Now here is the problem should i have even divide that -1 and switch the inequality signs? I could and I would get some meaningless answer like [tex]x \in (-\infty,-4)[/tex]
Anyways I threw it back in
[tex](-x-4)(x+2) > 0[/tex]
x is still 4, so no change, neither did the solution
So my solution remains as [tex]x \in (-4,-2)[/tex]