Please express in interval notation:
x < 0 or 7< x < 9
x < 0 or 7< x < 9
Split into two parts:
x < 0
(-∞,0)
i.e. from negative infinity to 0, excluding both limits using the parentheses.
7< x < 9
(7,9)
i.e. from 7 to 9, again excluding the two limits.
Now put them together with the union notation, ∪
(-∞,0) ∪ (7,9)
There is an alternative form for the interval notation for excluding the limits, i.e. instead of using parenthese, we could use brackets pointing to the exterior of the values, in the above example, we could write it as:
]-∞,0[ ∪ ]7,9[
(-∞,0) ∪ (7,9)
(-∞,0) ∪ (7,9)
or
]-∞,0[ ∪ ]7,9[
To express the given inequality in interval notation, we need to break it down into separate intervals, if applicable.
First, let's consider the expression "x < 0." This inequality states that x is strictly less than 0. In interval notation, we represent this as (-∞, 0), where "-∞" represents negative infinity and 0 represents the upper boundary that x cannot exceed.
Next, consider the expression "7 < x < 9." This means that x is greater than 7 and less than 9. In interval notation, we express this as (7, 9).
Combining both intervals, the final expression in interval notation is: (-∞, 0) U (7, 9). Here, U denotes the union of the two separate intervals.