some modulus questions

[yan03]

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

[jemidiah]

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!

[yan03]

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.

[jemidiah]

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