Solve the Inequality
I always like to see what's going on with these sorts of equations before I get lost in the algebra.
So here's what I'd do:
Draw a graph of . It's easy to do .... just draw and reflect in the x-axis the part below the x-axis. Don't be too fussed about where the x-intercepts are, by the way - they are unimportant.
Now draw a graph of .
It should be easy now to see that the line y = 2 cuts at four points. If you know the x-coordinates of those four points you can easily construct the intervals over which .....
You can see from the graph when you want to solve and when you want to solve in order to get those x-intercepts.
This is a simple linear inequality. In some ways it essentially boils down to what I've suggested, but I think you're applying the method in a superficial way - without really understanding why it works. That will cause trouble when ......
Things get more complicated with quadratic inequalities. Are you having trouble applying the method I suggested?
(I know it's late to post but I leave another way, and of course, it may help someone else.)
Inequality equals Consider the left inequality and rearrange it to From here we have First solution
Let's check the another inequality. (Which is easier to tackle.) Hence, our final solution will be given by (here we only need the axis for better understanding)