Question

Solve the system of equations :
$\frac{x}{2x+1}⩾\frac{1}{4},\frac{6x}{4x-1}<\frac{1}{2}$

Answer 1

$\frac{x}{2x+1}\ge \frac{1}{4},\frac{6x}{4x-1}<\frac{1}{2}$

$4x\ge 2x+1,12x<4x-1$

$\Rightarrow 2x\ge 1,8x<-1$

$\Rightarrow x\ge \frac{1}{2},x<-\frac{1}{8}$

$\Rightarrow x\in [\frac{1}{2},\infty )$ and $x\in (-\infty ,\frac{-1}{8})$.