How do you solve the inequality x²+x>1. I can not remember how to factor it. It doesnt make sense to me how you can have a single x and a negative 1
(Take a look at the graph I have attached.)
We are looking for the portion of the x-axis where the graph is above the x-axis.
We do this algebraically by the following process.
Solve
according to the quadratic formula.
Now break the x-axis into three parts:
We want to test the inequality on each of these intervals. The idea is to pick the easiest number in the interval to do the test on, so for example pick -100000000000000 in the first interval, pick 0 in the second, and pick 100000000000000 in the last interval. (Or any other numbers you like.)
: Check!
: Nope!
: Check!
So the solution set is .
-Dan