Solve for the values of $x$ in $|x+k|=|x|+k$ where $k$ is a positive real number The question asks me for which values of the real number $x$ is $|x+k|=|x|+k$ where $k$ is a positive real number.
How do I go about this? Can I square both sides to get rid of the absolute value signs? When I do it this way, I get a single $x$ sandwiched in the middle of a quadratic equation which I don't know what to do with, after I square and expand $|x|+k$. Is there another way of solving this problem?

Take the cases:
1) $\text{if}\ \ \ \ \ x>k$ ;
2)$\text{if}\ \ -k\leq x\leq k\\(x>0\ \ \text{or}\ \ x<0)$ ;
3)$\text{if} \ \ \ \ \ x< -k$ ;
Then simplify.
