Question

Solve:$37-(3x+5)\ge 9x-8(x-3)$ when $x$ is an integer.

Answer 1

$37-(3x+5)\ge 9x-8(x-3)$

$\Rightarrow 37-3x-5\ge 9x-8x+24$

$\Rightarrow 32-3x\ge x+24$

$\Rightarrow 32-3x-x\ge x+24-x$

$\Rightarrow 32-4x\ge 24$

$\Rightarrow 8-x\ge 6$

$\Rightarrow -x\ge 6-8$

$\Rightarrow -x\ge -2$

$\Rightarrow x\le 2$

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