# Homework Help: Pretty simple ordered field question

1. Apr 16, 2012

### jaqueh

1. The problem statement, all variables and given/known data
basically proving multiplying a negative number through an inequality changes the inequality

2. Relevant equations
if a > b, and c < 0,
then the following inequality holds: ac < bc.

3. The attempt at a solution
I am pretty stumped on this one, i tried to prove that C is a negative number, but i dont know where to go at all

2. Apr 16, 2012

### Hurkyl

Staff Emeritus
For the most part, it should be just unraveling definitions, and making use of the fact ad>bd for any positive d. (and picking a useful d)

3. Apr 16, 2012

### jaqueh

i'm still stuck, all i can think of is making the d=-c which i define when c+(-c)=0

4. Apr 16, 2012

### jaqueh

i'm still lost, i dont know why i am so bad at simple algebraic manipulations. can anyone offer more hints?

5. Apr 16, 2012

### Hurkyl

Staff Emeritus
So make the substitution. How is < defined? Apply the definition both to this case, and to the case you're trying to solve, so that you can see what you need to prove.

6. Apr 16, 2012

### jaqueh

I actually ended up figuring it out, thanks tho!

7. Apr 16, 2012

### Hurkyl

Staff Emeritus
Ah good!