For me (C) as well.
I prefer to draw a XY plan and identify the points (X,Y) such that the equations alone and then together are verified. I believe it's very fast
<=> y < x + 2 : it means that we consider all points (x,y) that are "under" the line x+2.
I represent the area in green in Fig-1. As we can see, the whole cadran (IV) is in the area, a cadran where x > 0 and y < 0. Thus, x*y < 0.
Meanwhile, part of cadran (I) is covered, in which x > 0 and y > 0. For this case, x*y > 0.
<=> y > x/2 + 3 : it means that we consider all points (x,y) that are "above" the line x/2 + 3
I represent the area in green in Fig-2.
We can see here:
o Part of cadran (II) is covered. That means x < 0 and y > 0 and so x*y <0
o Part of cadran (I) is covered. That means x > 0 and y > 0 and so x*y >0
Using (1) and (2):
We have to be at same time "under" the line x+2 and "above" the line x/2 + 3. I used a "flashy" green colour to reperesent the area.
Thus, the area is only a part of the cadran (I) where x > 0 and y > 0. Thus, x*y > 0
Fig-1_y-inf-to-x+2.jpg [ 19.2 KiB | Viewed 393 times ]
Fig-2_y-sup-to-x-div-2+3.jpg [ 17.03 KiB | Viewed 394 times ]
Fig-3_both.jpg [ 22.67 KiB | Viewed 394 times ]