Question 426014
Assume z different from 5. Multiply both sides of inequality by (z-5)

 {{{(z-5)*(z)/(z-5)>=2z(z-5)}}}

 {{{z>=2z^2-10z}}}

  {{{2z^2-11z<=0}}}

 {{{z*(2z-11)<=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^2}}}. 
Since this coefficient is positive the solution of our inequality is the closed interval: [0,11/2].