Solving Calculus Doubts: My Attempt

[Portuga]

The problem, and my attempt to solve it is here:
https://meocloud.pt/link/bf620660-aaf0-48ad-abfe-ac49f7ea0843/calculus_doubt.pdf/

 

[andrewkirk]

It's almost right. The only problem is that $k$ may be negative. So multiplying the inequality by $k$ will change direction of the inequality, which will prevent reaching the conclusion.

Two ways to get around this are:

1. Do three separate cases, for k positive, negative and zero respectively; or
2. Multiply by $|k|$ instead.

2 is quicker, but you'll need to insert a few careful steps around where you multiply by $|k|$ to ensure that each one is valid.

 

[Portuga]

Thank you very much!