Question

Solve
$2x\le x-1<3x+5$.

Answer 1

We have

$2x\le x-1\le 3x+5$

$\left(i\right)2x\le x-1$

$2x-x<-1$

$x<-1$

$\left(ii\right)x-1\le 3x+5$

$x-3x-1\le 5$

$-2x-1\le 5$

$-2x\le 4$

$x\ge -\frac{4}{2}$

$x\ge -2$

$\therefore -2\le x<-1$

Hence this is the answer.