Answer
$\dfrac{5}{6}$ $,$ $1$ $,$ $\sqrt{5}$ $,$ $3$ $,$ and $5$ satisfy the inequality
Work Step by Step
$-2+3x\ge\dfrac{1}{3}$ $;$ $S=\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\}$
$x=-5$
$-2+3(-5)\ge\dfrac{1}{3}$
$-2-15\ge\dfrac{1}{3}$
$-17\ge\dfrac{1}{3}$ False
$x=-1$
$-2+3(-1)\ge\dfrac{1}{3}$
$-2-3\ge\dfrac{1}{3}$
$-5\ge\dfrac{1}{3}$ False
$x=0$
$-2+3(0)\ge\dfrac{1}{3}$
$-2\ge\dfrac{1}{3}$ False
$x=\dfrac{2}{3}$
$-2+3\Big(\dfrac{2}{3}\Big)\ge\dfrac{1}{3}$
$-2+2\ge\dfrac{1}{3}$
$0\ge\dfrac{1}{3}$ False
$x=\dfrac{5}{6}$
$-2+3\Big(\dfrac{5}{6}\Big)\ge\dfrac{1}{3}$
$-2+\dfrac{5}{2}\ge\dfrac{1}{3}$
$\dfrac{1}{2}\ge\dfrac{1}{3}$ True
$x=1$
$-2+3(1)\ge\dfrac{1}{3}$
$-2+3\ge\dfrac{1}{3}$
$1\ge\dfrac{1}{3}$ True
$x=\sqrt{5}$
$-2+3\sqrt{5}\ge\dfrac{1}{3}$
$4.7082\ge\dfrac{1}{3}$ True
$x=3$
$-2+3(3)\ge\dfrac{1}{3}$
$-2+9\ge\dfrac{1}{3}$
$7\ge\dfrac{1}{3}$ True
$x=5$
$-2+3(5)\ge\dfrac{1}{3}$
$-2+15\ge\dfrac{1}{3}$
$13\ge\dfrac{1}{3}$ True
