17: The conditions give (in the same order):

• This condition is already solved.

• This condition is true for

  

  When solving these double inequalities, the knowledge of sign of x is essential. Since we have no info on it, we need to try both cases. Note that also the knowledge of the signs of the factors outside is important, so one has to also worry about what happens for what k.

  If x < 0, one gets

  

  assuming that k < 0. This has to be intersected with the condition x < 0. What about k = 0?

  If x > 0, one gets

  

  assuming that k < 0. This has to be intersected with the condition x > 0. What about k = 0?

Now make a union of these possibilities.

Answer