SOLUTION: Hi! Could you solve this inequalitiy and show me the steps please? {{{2/(-x+3)<=2/(-x)}}} Thank you!

Algebra ->  Inequalities -> SOLUTION: Hi! Could you solve this inequalitiy and show me the steps please? {{{2/(-x+3)<=2/(-x)}}} Thank you!      Log On


   

Question 401391: Hi! Could you solve this inequalitiy and show me the steps please?
2%2F%28-x%2B3%29%3C=2%2F%28-x%29
Thank you!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Fx+-+2%2F%28x-3%29%3C=+0 <==> 1%2Fx+-+1%2F%28x-3%29%3C=+0
<==> %28x+-+3+-+x%29%2F%28x%28x-3%29%29+%3C=+0 ==> 1%2F%28x%28x-3%29%29+%3E=+0
The critical numbers of the inequality are 0 and 3.
At the interval (-infinity, 0), 1%2F%28x%28x-3%29%29+%3E=+0.
At the interval (0,3), 1%2F%28x%28x-3%29%29+%3C+0.
At the interval (3, infinity), 1%2F%28x%28x-3%29%29+%3E=+0.
The critical numbers 0 and 3 don't satisfy the inequality.
Therefore the solution set is (-infinity, 0)U(3, infinity).