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?

If $x\ge0$ and $x+k\ge0$, then the identity holds always. You get $x\ge0$ and $k\ge-x$.
If $x\ge0$ and $x+k<0$, then $-x-k=x+k$, and $x+k=0$ (impossible).
If $x<0$ and $x+k<0$, then $-x-k=-x+k$, and $k=0$ (impossible).
If $x<0$ and $x+k\ge0$, then $x+k=-x+k$, and $x=0$ (impossible).
