The solution set of the inequation $4x + 3y > 5$ is

The inequality $4x + 3y > 5$ divides the xy-plane into three parts: points on the line $4x + 3y = 5$ (the boundary), points on one side of the line, and points on the other side of the line.

The inequality symbol is ">" (greater than), not "≥" (greater than or equal to). Points that lie exactly on the line $4x + 3y = 5$ are not part of the solution. This represents an open half-plane where the boundary is not included.

To determine which side of the line is the solution, test the origin $(0, 0)$.

Substitute $(x, y) = (0, 0)$ into the inequality:

$4(0) + 3(0) > 5$

$0 > 5$

This is false. The origin does not satisfy the inequality.

Since the origin is not in the solution set, the solution must be the half-plane on the opposite side of the line from the origin.

The solution is an open half-plane that does not contain the origin.