How do you solve #(x+4)/x>0#?

1 Answer
Apr 10, 2018

Answer:

Either #x>0# or #x<-4#

Explanation:

We can multiply both sides of the inequality by #x^2# to get

#x(x+4) > 0#

Note that we multiply by #x^2# since it is always positive and multiplying by a positive quantity does not change the sign of the inequality (on the other hand, multiplying by #x# would have lead apparently to #x+4<0#, which is wrong!)

Now, for #x(x+4)>0#, either both factors have to be positive, or both have to be negative. In the first case, #x# has to be greater than 0, in the second, it has to be smaller than -4.