Question

Solve the following equation:
$\left|x\right|-|x-2|=2$

Answer 1

given equation is

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

now it has 3 cases

$i.)x<0,ii.)0<x<2,iii.)x>2$

the respective equations in 3 cases are

$i.)-x-(2-x)=2,ii.)x-(2-x)=2,iii.)x-(x-2)=2$

therefore

in first case we get

$-2=2$ so no soution

in second case we get

$2x=4$ so $x=2$

in third case we get

$2=2$ therefore possible for every value of x greater then 2

so the solution is $x\ge 2$