Equations with Absolute Values: Absolute value on both sides of the equation

$|x+2|=|x-2|$

$x=0$

$|x-1|=|2x+3|$

$x=-4$ , $x=-\frac{2}{3}$

$|-x+6|=|3x-2|$

$x=-2$ , $x=2$

$|2x-6|=|-x+4|$

$x=3\frac{1}{3}$ , $x=2$

$|x+3|=|2x+6|$

$x=-3$

$|x+4|=|2x+20|$

$x=-8$ , $x=-16$