Question

Solve the system of inequalities:$|2x-3|\le 11,|x-2|\ge 3$

Answer 1

$|2x-3|\le 11,|x-2|\ge 3$

$-11\le 2x-3\le$, $-3\ge x-2\ge 3$

$-8\le 2x\le 14$ , $-1\ge x\ge 5$

$x\in [-4,7]$ and $x\in (-\infty ,-1)\cup [5,\infty ]$

$\therefore x\in [-4,-1]\cup [5,7]$