Answer
$-5$ $,$ $-1$ $,$ $\sqrt{5}$ $,$ $3$ and $5$ satisfy the inequality
Work Step by Step
$\dfrac{1}{x}\le\dfrac{1}{2}$ $;$ $S=\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\}$
$x=-5$
$\dfrac{1}{-5}\le\dfrac{1}{2}$
$-\dfrac{1}{5}\le\dfrac{1}{2}$ True
$x=-1$
$\dfrac{1}{-1}\le\dfrac{1}{2}$
$-1\le\dfrac{1}{2}$ True
$x=0$
$\dfrac{1}{0}\le\dfrac{1}{2}$ Left side undefined. False
$x=\dfrac{2}{3}$
$\dfrac{1}{(\frac{2}{3})}\le\dfrac{1}{2}$
$\dfrac{3}{2}\le\dfrac{1}{2}$ False
$x=\frac{5}{6}$
$\dfrac{1}{(\frac{5}{6})}\le\dfrac{1}{2}$
$\dfrac{6}{5}\le\dfrac{1}{2}$ False
$x=1$
$\dfrac{1}{1}\le\dfrac{1}{2}$
$1\le\dfrac{1}{2}$ False
$x=\sqrt{5}$
$\dfrac{1}{\sqrt{5}}\le\dfrac{1}{2}$
$0.4472\le0.5$ True
$x=3$
$\dfrac{1}{3}\le\dfrac{1}{2}$ True
$x=5$
$\dfrac{1}{5}\le\dfrac{1}{2}$ True
