Mathematico | Mathematico

The equation

| 3 - x | = \frac{x + k}{2}

has exactly two solutions.

Find the range of possible values of $k .$

By considering the diagram above, you can see that $k$ controls the vertical position of the line

y = \frac{x + k}{2}

If you can find the critical value which causes there to be exactly one solution, then you can find the range of values for which there are two solutions.