Can someone explain the basics of inequalities to me. I'm having trouble with the easiest of questions, just because the signs. For example: From here I have no idea what I'm doing. Can someone explain to me what to do after this point? I know it is something to do with negatives and positives. If someone could explain that to me I'd probably understand these a lot more. Thats my biggest issue.
Well, once again you have a "<" so you are looking for all points on the graph below the x-axis. (I never said it, but when setting up a problem like this you always want to get the RHS to be 0.)
So the only trick is to see where
for
.
So the solution set will be .
(The hyperbola moves from negative to positive over the vertical asymptote x = 3, if that's what's bothering you.)
-Dan
Oh yeah was the variable used in my book instead of . It is still a little confusing though, sadly. I don't know why but from the looks of the graph it looks like the opposite of what I listed the answers as above. But I'm going to listen to you anyways.
(x+1)(x-2)(x-3)< 0
The solution range are -1, 2, 3 by using number line method.
________-____+_______-___
| | | | | | | | | | | | | | | |
-2-1 01 2 3
Since
(x +1)(x-2)(x-3)=0
Substitute -2 into x in quadrate equation.
(-2 +1)(-2-2)(-2-3) = -1* -4* -5 = -20
x< -1, -1< x< 3, x >3.
The inequality solution is x < -1 and x > 3
from clement
cokhale@yahoo.com