First, isolate y from the equation of the boundary line:
[tex]\begin{gathered} 2x+2y=-10 \\ \Rightarrow2y=-10-2x \\ \Rightarrow\frac{2y}{2}=\frac{-10-2x}{2} \\ \Rightarrow y=-5-x \end{gathered}[/tex]
Notice that the shaded region corresponds to the points that satisfy that the y coordinate is lower than the value of the expression -5-x.
Therefore, the inequality that represents the region in the graph, is:
[tex]y<-5-x[/tex]
