How do we express this in interval notation?
x < 0 or 7 < x < 9
[-∞,0) &cup (7,9)
(-∞,0) &cup (7,9)
To express the inequality x < 0 or 7 < x < 9 in interval notation, you would write it as two separate intervals using the union symbol (∪) to connect them.
The interval for x < 0 would be written as (-∞, 0), where -∞ represents negative infinity and 0 represents zero. This interval includes all values less than 0 but does not include 0 itself.
The interval for 7 < x < 9 would be written as (7, 9), which includes all values greater than 7 and less than 9, but does not include 7 or 9.
Putting it together, the expression in interval notation would be (-∞, 0) ∪ (7, 9). This represents all values of x that are less than 0 or between 7 and 9, excluding 0, 7, and 9.
To express the given inequality in interval notation, you need to break down the intervals separately, based on the conditions given.
First, the inequality "x < 0" represents all values of x that are less than 0, but not including 0. In interval notation, this is expressed as (-∞, 0).
Next, the inequality "7 < x < 9" represents all values of x that are greater than 7 and less than 9. In interval notation, this is expressed as (7, 9).
To combine the two intervals, use the union symbol (∪) to indicate that the intervals are separate and not overlapping. Therefore, the interval notation for the given inequality is (-∞, 0) ∪ (7, 9).