SOLUTION: Express set of numbers using interval notation and set-builder notation: numbers more than 2 units from 8 we were coming up with: x|6<x>10; but my daughter says her teacher sa

In order to be more than 2 units away from 8, a number must
be either left of 6 OR right of 10.  So the graph is

<============================o-----------o==================>
 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15

In interval notation that is 

(-,6) U (10,)

and the set builder notation is:

{x | x < 6 OR x > 10}

But since your teacher says the symbols must go in
the same direction, then we can do either of two
things. We can change the 

x < 6

to 

6 > x, which is the same thing,

and make it 

{x | 6 > x OR x > 10}

or else we can change the 

x > 10

to 

10 < x, which is the same thing,

and make it 

{x | x < 6 OR 10 < x}

But most teachers would not require
both symbols to go the same way.

Edwin