## blackbird02 one year ago Help in proving this inequality using the concepts or theorems on the properties of real numbers

1. blackbird02

2. blackbird02

Prove that if a>0, b<0, then $ab+\frac{ b }{ a }<0$

3. triciaal

|dw:1442641989956:dw|

4. blackbird02

what does ve stand for?

5. triciaal

sorry, -ve = negative and +ve = positive

6. blackbird02

I'm sorry, but I still don't get it. What would be my starting equation in the proving?

7. zzr0ck3r

$$ab<0 \text{ and } \frac{a}{b}<0$$ so $$ab+\frac{a}{b}<0$$

8. blackbird02

@zzr0ck3r How would I prove this using the concepts or theorems on the properties of real numbers?

9. blackbird02

@Hero any idea how to prove this?

10. Hero

Are you still here.

11. blackbird02

Yeah

12. Hero

13. blackbird02

@Hero just a clarification, in the seventh row, what is the equation? is it ab<0 +b/a<0 Or b/a<0 should be on another line?

14. Hero

It's one line: Two inequalities being added together

15. blackbird02

Oh, okay. I get it now. Thank you so much!

16. Hero

It's written exactly as it Should be

17. triciaal

@hero can you explain the step where you have "flip sign"?

18. Hero

b is negative If you multiply both sides of a>0 by a negative number, you have to invert the inequality symbol

19. blackbird02

@Hero Thank you so much!

20. triciaal

sorry, well thanks but that's the only place we differ on why a negative times a positive is negative. multiplication is group addition and we have a constant times a negative entity so it is more negative.

21. zzr0ck3r

22. triciaal

@zzr0ck3r yes example 3 * 2 = 2 + 2 + 2 etc

23. triciaal

24. zzr0ck3r

addition is the operation on the reals as a group multiplication is the other operation on the reals as a ring

25. zzr0ck3r

how would you write out (1/2)*(1/3) in those terms?

26. triciaal

what?

27. zzr0ck3r