Interval notation corresponding to one inequality is developed as follows:
The lower bound of the inequality is 7, since all values of x must be greater than or equal to 7.
So we start with
[7,
which means that 7 is the lower bound of the interval and 7 is included.
If the problem were x>7, then we would use
(7,
to indicate that 7 is not part of the interval.
All values of x greater than 7 are part of the interval. So there is no upper limit.
We write this as
[7,∞)
and that's it.
If there were an upper bound, say 9, you would write
[7,9] if 9 were included in the set, or [7,9) if 9 were not included.
If the problem were x≤7, then use
(-∞,7]
We always use parentheses for infinity, whether positive or negative, because infinity is unbounded.
If we had more than one interval, we would use union symbols.
Example: x<3 or x≥8
(-∞,3) ∪ [8,∞)
