x<3 or x>6 in interval notation

Question

how do you write the above problem in interval notation

Answer 1

Interval notation uses pairs of numbers and square or rounded brackets.

 

(0,1)

 

means the interval from zero to one, not including zero or one

 

[0,1]

 

means the interval from zero to one, including both zero and one

 

Finally, multiple intervals can be included with a union symbol. The interval from -10 to 0 including zero OR from 1 to 5 including one would be written as:

 

(-10,0]∪[1,5)

 

For your answer, we want all numbers less than three or all numbers greater than six. If they had used a less than or equal to, then we would have to use square brackets. For the lower end, I'm going to use negative infinity. We can never actually include infinity or negative infinity, so it is always a rounded bracket:

 

(-∞,3)∪(6,∞)