Korzystając ze wzoru na kwadrat różnicy mamy: 

${\left(4x-6\right)}^2\ge {\left(6x-4\right)}^2$  

${\left(4x\right)}^2-2\cdot 4x\cdot 6+6^2\ge {\left(6x\right)}^2-2\cdot 6x\cdot 4+4^2$  

$16x^2-48x+36\ge 36x^2-48x+16$  

$16x^2-48x+36-36x^2+48x-16\ge 0$  

$-20x^2+20\ge 0\mid :\left(-20\right)$  

$x^2-1\le 0$  

$\left(x+1\right)\left(x-1\right)\le 0$  

$x+1=0\vee x-1=0$  

$x=-1\vee x=1$    

$\mathbf{x}\in <-1;1>$