I have two inequality questions that I need help solving:
As you can see, i've ended up with all the different inequalities but when I combine then I get the wrong answer.
help me please!
Here's the first one.
. . Your punchlines are a bit off . . .
The left side: .
We have: .
There are two cases:  both factors are positive,  both factors are negative.
The right side: .
There are two cases:  the factors are (-)(+),  the factors are (+)(-).
To determine the final solution, I had to make pretty pictures . . .Code:x < 1 or x > 4 = = = = o - - - - - o = = = = 1 4 -1 < x < 5 - - o = = = = = = = = = = = o - - -1 5
Combining them, we have:
Code:- - o = = o - - - - - o = = o - - -1 1 4 5
For the second one... ouch !
Note that . Therefore, this is always negative !
And remember, when you multiply an inequality by a negative number, its direction is changed. This means that if you multiply both sides by , you'll have :
Now, see the two situations (if x<0) and (if x>0)
If you're not sure, you can do the special case x=0...
Thanks Soroban and Moo. I get what I was doing wrong and thanks!
I was comparing my worng answers with the worked solutions I had on another piece of paper. I couldn't follow their method since they were doing some odd stuff with moduli (not that odd now i'm comparing it with correct answers ).