Write the solution set of /x-3/>5 in set builder notation

We'll have to solve the double
inequality:

-5>x-3>5

We'll
solve the first, left, inequality and we'll apply the symmetric
formula:

x - 3 <
-5

We'll add 3 both sides:

x
< -5 + 3

x <
-2

x belongs to the interval of values: (-infinite,
-2)

We'll solve the right
inequality:

x - 3 >
5

We'll add 3 both sides:

x
> 5 + 3

x > 8

x
belongs to the interval (8, +infinite).

The
common solution of the system is the empty set since there is no value for x to satisfy
both inequalities at the same time.