Inequality/interval notation question

Question

Let S be
(−∞,3]∪[15,∞)

Then S can also be described in set notation by the inequality
|x−a|≥b

 

a=?

b=?

Answer 1

l x-a l ≥ b means that x-a ≥ b or x-a ≤ -b (if b > 0)

 

So, x ≥ a+b or x ≤ a-b

 

Therefore, we need to solve the system a + b = 15

                                                          a -  b = 3

 

Adding the equations, we get 2a = 18.  So, a = 9 and b = 6

 

Another approach is to notice that 9 is halfway between 3 and 15 (so, a = 9) and the distance from 3 to 9 and the distance from 9 to 15 is 6 (so, b = 6).