Use Interval Notation to define each interval:
All real numbers at least 5 units from 8.
well x can not be in the part of our number line from 3 to 13 but 3 and 13 are ok
3 >/= x >/=13
(-oo,3] U [8,+oo)
(-oo,3] U [13,+oo)
To define the interval of all real numbers at least 5 units from 8 using interval notation, we can express it in two separate intervals:
1. Interval from negative infinity up to 3: (-∞, 3]
This interval includes all real numbers that are less than or equal to 3 units away from 8. Since we are looking for numbers that are at least 5 units away from 8, this interval includes all numbers less than 3 units away as well.
2. Interval from 13 to positive infinity: [13, ∞)
This interval includes all real numbers that are greater than or equal to 13 units away from 8. Again, since we are looking for numbers that are at least 5 units away from 8, this interval includes all numbers greater than 13 units away as well.
Therefore, the interval notation to define all real numbers at least 5 units away from 8 is (-∞, 3] ∪ [13, ∞).