Solve the inequality

x-5/3-x less than 0

ok this is what i got

x-5=0

x=5

3-x=0

x=3

my test intervals were (infinity, 5) (5,3) (3,infinity)

what is my solution set???

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- Nov 9th 2009, 10:44 PMflexusSolve the inequality
Solve the inequality

x-5/3-x less than 0

ok this is what i got

x-5=0

x=5

3-x=0

x=3

my test intervals were (infinity, 5) (5,3) (3,infinity)

what is my solution set??? - Nov 10th 2009, 12:19 AMBacterius

- 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 . - Nov 10th 2009, 01:21 AMCaptainBlack
**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 - Nov 10th 2009, 02:37 AMHallsofIvy
(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. - Nov 10th 2009, 06:28 AMflexus
so what is my solution set???

- Nov 10th 2009, 07:09 AMGrandad