Question

Solve the following inequation and represent the solution set on a number line.
$-8\frac{1}{2}<-\frac{1}{2}-4x\le 7\frac{1}{2},xϵ1$.

Answer 1

$\Rightarrow$ $\frac{-17}{2}<\frac{-1}{2}-4x\le \frac{15}{2}$

adding $\frac{1}{2}$ to the inequation we get

$\Rightarrow \frac{-16}{2}<-4x\le \frac{16}{2}$

$\Rightarrow$ $-8<-4x\le 8$

dividing by $-4$ we get

$\Rightarrow 2>x\ge -2$

hence the solution set of the inequation is

$[-2,2)$