Posted by Samantha on Tuesday, September 9, 2008 at 8:41pm.
I'm having trouble with inequalities. Basically my problem is about which way the sign goes. Here's an example..
X(X+1)>2
so then it becomes
X^2 + X>2
Correct? Then
X^2 + X  2>0
then factor so it becomes
(X+2)(X1)>0
And so I end up with X>2 and X>1 as my answer, but the book says it should be X<2. Why did the sign switch? I didn't divide by a negative did I? Can someone help me please?

Algebra  Reiny, Tuesday, September 9, 2008 at 10:12pm
Here is the logical analysis:
(X+2)(X1)>0 says that the answer is positive, so either
x+2 > 0 AND x1 > 0
x > 2 AND x > 1 > x > 1
or
x+2 < 0 AND x1 < 0
x < 2 AND x < 1 x < 2
so x < 2 OR x > 1
I use the following quick way to solve these kind of problems.
from (X+2)(X1)>0
the "critical values", or the solution to the corresponding "equation", are
x = 2 and x = 1
put these values on a number line, this will split the number line into 3 regions
1. x < 2
2. x between 2 and 1
3. x > 1
select any value of x in those regions and test it in your factored inequation.
e.g. for
1. I picked x=5 that works
2. let x = 0 , does NOT work
3. let x = 10 , that also works
so x > 1 OR x < 2