some modulus questions

http://www.freewebs.com/yan_kong/3.jpg
http://www.freewebs.com/yan_kong/4.jpg
http://www.freewebs.com/yan_kong/5.jpg
http://www.freewebs.com/yan_kong/test1.jpg

I just want to check my answers with you guys. I'm not sure of my answers

If you showed us your current work I'd be happy to go over it, but I'm a little anxious about answering questions on a quiz you may or may not have submitted. Sorry!

lol. okey.
number 5 answer is D

For 3, I got A as answer.

For the other questions, I just eliminated the denominator but a friend of mine is telling me to multiply both side by the (dominator)^2.
Just eliminating the denominator seems too simple to do.
I'm a little unsure about my friend's theory; the left hand side can be practically anything.

3. A: Let x-> -1.5 and you'll see the counterexample immediately.
4. -2 < x < -1. See 4* for the work/reasoning.
5. D: Let x-> 2 and you'll see immediately that the other functions just don't work.
6. Apply the reasoning from 4* and you'll get these two. Alternatively, you can just graph the functions (this is probably easier).


4*. First off, the inequality doesn't work whenever the denominator is 0, which happens at x = 2, and x = -2. So, x cannot be 2, or -2.

With that in mind, you can multiply both sides by the denominator, but you MUST remember that multiplying by a negative number flips the direction of the inequality.

So, when is the denominator positive and when is it negative? When x > -2, the denominator is positive; negative otherwise (note that x <> +/- 2).

Thus, for x > -2, the inequality becomes x+1 < 0 or x < -1. Both of these are satisfied only for -2 < x < -1

Thus, for x < -2, the inequality becomes x+1 > 0 or x > -1. Both of these are satisfied, well, never.

So the solution is just -2 < x < -1