First step in graphing the solution of linear inequality is to draw the line of corresponding equation. The corresponding equation in this case is y = x/2 - 4.
The line is plotted already in the given options, we have to chose which side of the line will be the solution region for the given inequality. For this purpose take any point, substitute its value in the given inequality. If the inequality is satisfied, then the side on which the point lies is the solution region else the other side will be the solution.
So, for this case, we can substitute the point (0,0) in the given inequality. The inequality will be:
0 < 0 - 4
0 < -4
this is false, so the region above the line is not the solution region. The region below the line is the solution region. So option A is the correct answer.
