Rational Inequality

Question

x+45/x<14

Answer 1

if x > 0: 

times x both sides:

x^2 + 45 < 14x

x^2 - 14x + 45 < 0

(x-5)(x-9) < 0

5 < x < 9  -- good for x > 0

 

if x < 0:

times x both sides:
x^2 + 45 > 14x
x^2 - 14x + 45 > 0
(x-5)(x-9) > 0
x < 5 or x > 9

and x < 0

so x < 0

 

 

So 5 < x < 9 or x < 0