The equations of the lines are correct.
To test the shading test any point in the shaded area
Using the point (3, 1) let’s substitute for x and y in both inequalities:
1 < 2 x 3 - 3 is true
1 >= -1/2 x 3 + 2 = 1/2 is true
Therefore your equations also correctly describe the shading.
I guess we should also test points in the other three regions but they will fail in one or both inequalities.
