- If eg. eg. , then the inequality is reversed :
- If eg. eg. , then the inequality is not reversed :
Therefore, your fraction will be lesser than for and .
How bacterius' post should have looked:
Your inequality is:
Case 1
If (which is equlvalent to ) the inequality becomes:
or
So the inequalityholds for
Case 2
If (which is equlvalent to ) the inequality becomes:
or
So the inequality holds for
Combining these two cases we have the inequality holds when or
CB
(5,3)? Surely you know that 3< 5! Your test intervals are (-infinity, 3), (3, 5), and (5, infinity). Now just test one number in each interval.
0 is in (-infinity, 3) and (0- 5)/(3- 0)= -5/3< 0.
4 is in (3, 5) and (4-5)/(3- 4)= -1/-1= 1> 0
6 is in (5, infinity) and (6- 5)/(3- 6)= 1/-3= -1/3< 0.