Grammar I - 03.05  
 ~ませんか  
~ません  = the present tense negative verb, plus the question particle, can be used to extend an invitation.  
 ~masen ka?  
 

It should be noted that the affirmative counterpart of this (~ます か - ~masu ka) cannot be so used.  

   
ひるごはん を たべません か。  What do you say to having lunch with me? 
hirugohan o tabemasen ka?  

いい です ね。

Sounds great.
ii desu ne.  
   
テニス を しません か。 Will you play tennis with me?

tenisu o shimasen ka?

 
うーん、ちょっと。 "Um, it's slightly"
(inconvenient for me at this moment).

uun, chotto.