Question 1116168
Already was answered:
<a href="https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1115838.html">https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1115838.html</a>



Question 1115838
-----------------------------------------------
{{{2/x}}} is less than or equal to {{{x/2}}}.
-----------------------------------------------


{{{2/x<=x/2}}}

-

{{{2/x-x/2<=0}}}

{{{(2/x)(2/2)-(x/2)(x/x)<=0}}}

{{{4/(2x)-x^2/(2x)<=0}}}

{{{(4-x^2)/(2x)<=0}}}


{{{highlight_green(((2-x)(2+x))/(2x)<=0)}}}


The critical values of x can be found from that inequality.

These critical x values are  -2, 0, 2.


check the intervals on x in  {{{-infinity<x<=-2}}}, {{{-2<=x<0}}},{{{0<x<=2}}}, {{{2<=x<infinity}}}.
See in which intervals the ORIGINAL inequality is true and in which it is false.



TRUE FOR  {{{-2<=x<0}}} and for {{{2<=x<infinity}}}.