Answer
$-5$ $,$ $-1$ and $0$ satisfy the inequality
Work Step by Step
$1-2x\ge5x$ $;$ $S=\{-5,-1,0,\frac{2}{3},\frac{5}{6},1,\sqrt{5},3,5\}$
$x=-5$
$1-2(-5)\ge5(-5)$
$1+10\ge-25$
$11\ge-25$ True
$x=-1$
$1-2(-1)\ge5(-1)$
$1+2\ge-5$
$3\ge-5$ True
$x=0$
$1-2(0)\ge5(0)$
$1\ge0$ True
$x=\dfrac{2}{3}$
$1-2\Big(\dfrac{2}{3}\Big)\ge5\Big(\dfrac{2}{3}\Big)$
$1-\dfrac{4}{3}\ge\dfrac{10}{3}$
$-\dfrac{1}{3}\ge\dfrac{10}{3}$ False
$x=\dfrac{5}{6}$
$1-2\Big(\dfrac{5}{6}\Big)\ge5\Big(\dfrac{5}{6}\Big)$
$1-\dfrac{5}{3}\ge\dfrac{25}{6}$
$-\dfrac{2}{3}\ge\dfrac{25}{6}$ False
$x=1$
$1-2(1)\ge5(1)$
$1-2\ge5$
$-1\ge5$ False
$x=\sqrt{5}$
$1-2\sqrt{5}\ge5\sqrt{5}$
$-3.4721\ge11.1803$ False
$x=3$
$1-2(3)\ge5(3)$
$1-6\ge15$
$-5\ge15$ False
$x=5$
$1-2(5)\ge5(5)$
$1-10\ge25$
$-9\ge25$ False
