How does Lady Macbeth greet Duncan upon his arrival at Inverness (William Shakespeare's Macbeth)? 

Expert Answers
mwestwood eNotes educator| Certified Educator

When King Duncan arrives at Inverness Castle, Lady Macbeth greets the king in an unctuous, ingratiating manner.

All our service,
In every point twice done and then done double,
Were poor and single business to contend
Against those honors deep and broad wherewith
Your majesty loads our house. (1.6.14-18)
Lady Macbeth speaks to King Duncan in this manner in order to deceive the ruler into believing that they are grateful to him for Macbeth's new position as Thane of Cawdor. Lady Macbeth states that they have cleaned and prepared for the occasion of Duncan's arrival most thoroughly and they wish him to be comfortable in their house. This flattery is done in order to deceive King Duncan into thinking that Macbeth is a loyal subject and that he is fond of Duncan.
Before the king has entered Inverness, Duncan remarks that the castle of Macbeth "sweetly recommends itself" (1.6.2). However, the nobleman Banquo, who has been with Macbeth and witnessed the three witches and heard their predictions, is not so easily deceived, and he suspects the motives of the Macbeths because he knows what the other predictions of the witches have been, especially the one in which the witches tell Macbeth he will be king.
literaturenerd eNotes educator| Certified Educator

Lady Macbeth, in act one (scene six) of William Shakespeare's Macbeth, welcomes King Duncan into their (Macbeth's and her) home. She is overly welcoming. She states that everything has been double checked and double checked again in order to insure everything is in order for the king's visit. Duncan calls Lady Macbeth an honored hostess, and she proves to be very honorable (at least to his face). 

Lady Macbeth most likely greets the king by herself because Macbeth is most likely contemplating the murder of Duncan. Later, she will take Duncan to meet Macbeth (probably as what would be custom in the times).