SOLUTION: How can I solve this nonlinear inequality? {{{z/(z-5) >= 2z}}} Thank you very much!

Algebra ->  Inequalities -> SOLUTION: How can I solve this nonlinear inequality? {{{z/(z-5) >= 2z}}} Thank you very much!       Log On


   

Question 426014: How can I solve this nonlinear inequality?
z%2F%28z-5%29+%3E=+2z
Thank you very much!
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Assume z different from 5. Multiply both sides of inequality by (z-5)
%28z-5%29%2A%28z%29%2F%28z-5%29%3E=2z%28z-5%29
z%3E=2z%5E2-10z
2z%5E2-11z%3C=0
z%2A%282z-11%29%3C=0
The roots of this quadratic equation are {0,11/2 }. As we know in the closed interval [0,11/2] the equation has the opposite sign of the coefficient
beside
z%5E2.
Since this coefficient is positive the solution of our inequality is the closed interval: [0,11/2].