Thread: Inequalities.

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!

Hello, Showcase_22!

Here's the first one.
. . Your punchlines are a bit off . . .

The left side: .

We have: .

Factor: .


There are two cases: [1] both factors are positive, [2] both factors are negative.

. .

. .

Therefore: .



The right side: .

Factor: .


There are two cases: [1] the factors are (-)(+), [2] 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

Therefore: .

Hi

For the second one... ouch !

You have

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 ).