Question

Solve & graph the solution set of $-2<2x-4$ and $-2x+5\ge 13,xϵR$

Answer 1

$-2<2x-4$
$\Rightarrow 2x-4>-2and-2x+5\ge 13$
$\Rightarrow 2x>2and-2x\ge 13-5$
$\Rightarrow x>1and-2x\ge 8$
$\Rightarrow x>1and-x\ge 4$
$\Rightarrow x>1andx\le -4$
$\therefore x>1orx\le -4orx\in (-\infty ,-4)\cap (1,\infty )$