Question

Write the set of integers les than -6 or greater than 21 in set-builder notation. Write the interval in interval notation

Answer 1

the set of integers les than -6 or greater than 21

did you wrote it correct :

... < -6 or 21 < ...

?

Answer 2

|x-a|>b means
x-a<-b,x-a>b
or x<a-b,x>a+b
a-b=-6
a+b=21
add
2a=15
a=15/2=7.5
b=21-7.5=13.5
so
|x-7.5|>13.5
or
\[(-\infty,-6)U(21,\infty)\]