Posted by Amy~ on .
I don't get when you use "or" or "and" in inequalities.
Like for this quadratic inequality:
x^(2) +x 12 > 0
becomes x < 4
x > 3
why is the answer {xx<4 or x>3} and not {x3<x<4} ?

Math 
Henry,
Your quadratic inequality has TWO solutions: x < 4 AND x > 3.
The 2nd arrangement where you have x in the center of the inequality is normally used with compound inequalities. 
Math 
MathMate,
If you look at the graph, it would be clear that the part of the curve which is above the xaxis is in two separate parts, therefore the answer is
x<4 and x>3.
On the other hand if the question had been x^(2) +x 12 < 0 , then the solution will be continuous on the number line, namely 4<x<3.
See graph:
http://img529.imageshack.us/img529/2064/1285810976.png