Question

Solve:$2(2x+3)-10\le 6(x-2)$ when $x$ is a natural number.

Answer 1

$2(2x+3)-10\le 6(x-2)$

$\Rightarrow 4x+12-10\le 6x-12$

$\Rightarrow 2(2x+1)\le 2(3x-4)$

$\Rightarrow 2x+1\le 3x-4$

$\Rightarrow 2x-3x\le -4-1$

$\Rightarrow -x\le -5$

$\Rightarrow x\ge 5$

$\therefore x\in \{5,6,7,8,...\}$