a) We must solve the following compound inequality:
[tex]x-3<-9\text{ or }x+2\ge1.[/tex]
1) From the first inequality we have:
[tex]\begin{gathered} x-3<-9, \\ x<-9+3, \\ x<-6. \end{gathered}[/tex]
2) From the second inequality we have:
[tex]\begin{gathered} x+2\ge1, \\ x\ge1-2, \\ x\ge-1. \end{gathered}[/tex]
So we have that the compound inequality is equivalent to:
[tex]x<-6\text{ or }x\ge-1.[/tex]
Which can be written as:
[tex]x<-6,x\ge-1[/tex]
b) Graph of the compound inequality:
Answer
a. x < -6, x ≥ -1
b. Graph
