Question

Solve:$-(x-3)+4>-2x+5$ when $x$ is a integer.

Answer 1

$-(x-3)+4>-2x+5$

$\Rightarrow -x+3+4>-2x+5$

$\Rightarrow -x+7>-2x+5$

$\Rightarrow -x+7-7>-2x+5-7$

$\Rightarrow -x>-2x-2$

$\Rightarrow -x+2x>-2x-2+2x$

$\Rightarrow x>-2$

$\therefore x\in \{-1,0,1,2,3,...\}$