Question

Solve:$3(x-1)\le 2(x-3)$ when $x$ is an integer.

Answer 1

$3(x-1)\le 2(x-3)$

$\Rightarrow 3x-3\le 2x-6$

$\Rightarrow 3x-3+3\le 2x-6+3$

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

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

$\Rightarrow x\le -3$

$\therefore x\in \{....,-6,-5,-4\}$