Question

Absolute value equation |x-3|=x

Answer 1

When $x\ge3$, you have

$|x-3|=x\implies x-3=x\implies 0x=3$

which has no solution.

When $x$,

$|x-3|=x\implies -(x-3)=x\implies 2x=3\implies x=\dfrac32$