Given: The inequalities below
[tex]\begin{gathered} y-2<-5 \\ y-2>5 \end{gathered}[/tex]
To Determine: The solution set of the given inequalities
Solution
[tex]\begin{gathered} y-2<-5 \\ y<-5+2 \\ y<-3 \\ y-2>5 \\ y>5+2 \\ y>7 \end{gathered}[/tex]
Let us combine the two solutions
[tex]\begin{gathered} y<-3,y>7 \\ -3>y,y>7 \\ The\text{ solution is} \\ -3>y>7 \end{gathered}[/tex]
The graph is as shown below
