Given inequation is 2x + y > 5.

Now, we convert the inequation into an intercept line equation form, we can clearly see the intercepts of the inequation on x-axis and y-axis.

2x + y > 5

[dividing the whole inequation by 5]

Therefore, from the above inequation, we can say that, 2.5 and 5 are the intercepts of the x-axis and y-axis respectively.

Now by plotting these on the graph, we can clearly see the graph of the inequation.

From the graph, it is clear that, the solution set of the inequation

2x + y > 5 is the open half plane not containing origin i.e. option B.