Remark
You have to start with the equality equations first and then go to the inequalities.
Step One
Discuss y = 2x + 2. That boundary is a dotted line. That is because it is not included in the area defined by y < 2x + 2. You should also note that everything in this region is below that line. See the diagram on the left (below).
Step Two
Discuss x + y >= -3. This graph actually means y >=-x - 3 The line itself is the lower boundary of the inequality. It looks like the center graph.
Step Three
When you put the two graphs together, you get the diagram on the right. The mauve kind of color is the region you are interested in. (Mauve is a kind of red purple).
Answer
Lower Right
