solve 6/(x-4)-5/3

Question

solve 6/(x-4)>-5/3

hero · Answer

$\large\frac{6}{x-4} > -\frac{5}{3}$

hero · Answer

Hint: Cross Multiply to get:

6(3) > -5(x-4)

anonymous · Answer

yeah, I got x>2/5. but i was wondering what i should do if x was negative...i tried to just flip the sign but it wasnt an answer choice on my assignment

hero · Answer

If you did the steps correctly, you would end up with 

-2 > -5x

At this point, what you want to do is add 5x to both sides, while also adding 2 to both sides to get:

5x > 2

Then you could simply divide both sides by 5 to get:

x > 2/5

This is usually the case that students normally have trouble with, but I just showed you how to avoid the trouble.

anonymous · Answer

but (2/5, inifinity) isnt the entire solution...so i was wondering if you had to consider 2 different situations in this equation?

anonymous · Answer

(sorry for the hassle, inequalities are very confusing to me)

hero · Answer

$(2/5, 4) (4, \infty)$

since $x \ne 4$

hero · Answer

With inequalities of this type, you have to pay attention to the denominators of fractions, because the denominators of fractions can never equal zero. Good catch.