Originally Posted by
jam2011 can i use this:
since we have (3x-6)/(3-x)<0 then
case 1: suppose x is positive, x>0
No! you should be supposing that the entire denominator is positive.
Probably the examples your instructor used had "x only" in the denominator
(3x-6)/(3-x)>0 you've inadvertently switched the inequality, by imagining x>3
(3x-6)/(3-x)<0
3x-6>0 by multiplying 3-x both side
true if x>3, as the denominator is negative and we reverse the inequality
3x>6 by adding 6 both side
x>2
However, x must also be >3, so x>3 means x>2 also
Solution is x>3
Case 2 : when x is negative then x<0
You need x<3 so that the denominator is positive
(3x-6)/(3-x)<0
3x-6>0 by multiplying 3-x both side.... no
You don't switch the inequality this time because you are not multiplying by a negative number.
3x>6 by adding 6 both side
x>2
3x-6<0
3x<6
x<2
i use this pattern since this my instructor discussion? or i cannot apply it this time