Hi,
I would like to know how you solve inequalities of a cube function.
For example, (2x+1)(x+2)(x-3)>0.
I know how to factorise and how to get your roots (the points on the line), but my problem comes in with determining the order of the + and - between the roots. I was taught that the order of the + and -of any inequality will always start with a + on the left, and then alternate between + and -. I have come across this example where it is apparently not the case. The answer to this example indicates that the first sign on the left is in fact a negative.
- (-2) + (-0.5) - (3) + resulting in an answer of -2 < x < -0.5 or x >3.
The way I would have done it is:
+ (-2) - (-0.5) + (3) - resulting in a final answer of x<-2 or -0.5 < x < 3.
Why is this? What does the order of these signs actually mean?
Please help!
Thank you!