That's just a little question I have, and I can't find the answer on the web.
Find the solution set for
Now, the thing I have learned is to keep the left expression (or the right, it doesn't matter) and keep and inverse the sign of the other expression, changing the direction accordingly.
But if we are to get the squares of both sides we get:
Getting the roots here and looking at the sign of in the quadratic expression we can see that see that we are searching for x>0 values of x that will give a x<a u b<x interval. So the solution set is:
Now, calculating using the other method gave us the inverse interval.
So the direction of the inequality must change when we take the absolute value out.
Is this the correct way of doing it? Why is this possible?