Find the solutions of following inequalities graphically in a two dimensional plane. y + 8 > 2x

y + 8 = 2x

or y - 2x = -8

or 2x - y = 8 ...(i)
Putting x = 0, y = -8, therefore the point on the y-axis is (0, -8). The point on the x-axis is (4, 0). AB is the graph of (i).

Putting x = 0, y = 0 in the given inequality we have 0 + 8 ≥ 2(0) or 8 ≥ 0, which is true. Hence origin lies in the half plane region I.

Clearly, any point on the line satisfy the given inequality.

Hence, the shaded region I including the points on the line is the solution region of the inequality.