Question

Find the integer values of $x$ for which $x-7\le 4x\le 5+2x$.

Answer 1

$x-7\le 4x\Rightarrow 4x\ge x-7\Rightarrow 3x\ge -7\Rightarrow x\ge \frac{-7}{3}\simeq -2.33$

and $4x\le 5+2x\Rightarrow 2x\le 5\Rightarrow x\le \frac{5}{2}=2.5$

$\Rightarrow$ Integral values of $x=-2,-1,0,1,2$