x|x-3|<2
I did x(x-3)<2 or x(x-3)<2 and simplified it to x^2-3x<2 and am not sure how to simplify it further and express it in interval notation. Help!
your x(x-3)<2 or x(x-3)<2 are the same expression
did you mean:
x(x-3)<2 or x(3-x)<2 ?
some preliminary...
clearly any negative value of x will work,
since -(+) is negative which is < 2
notice that is true for all x < 1
so x < 1
also if x = 2, we have
2|-1| = 2
and 2 < 2 is false,
so for x > 2 we might have some cases
if x^2 - 3x - 2 < 0
let's solve x^2 - 3x - 2 = 0
x = (3 ± √17)/2
= appr 3.56 or appr -.56 , but the -.56 is included in the x<1 situation
so x < 1 OR 2 < x < 3.56
I will let you put that in interval notation, not a big fan of that notation, the notation I use is much more explicit
see graph by Wolfram
http://www.wolframalpha.com/input/?i=x%7Cx-3%7C%3C2