Write the inequality in interval notation. Then graph the interval. x <= - 2 or x > 0 Write the inequality in interval notation. Choose the correct answer below. OA. (- ∞, - 2) and (0, ∞) OC. [- 2, 0] OB. [- 2, 0) OD. (- ∞, - 2] * or(0, ∞)
The inequality is x <= -2 or x > 0.
In interval notation, the solution is (-∞, -2] U (0, ∞).
So the correct answer is OD. (-∞, -2] U (0, ∞).
Here is the graph of the interval:
The interval starts at negative infinity and goes up to and includes -2, then it has a gap, and then it starts at 0 and goes to positive infinity.
-------------------------○--------------○------------------->
-∞ -2 0 +∞
The correct answer is OA. (- ∞, - 2) and (0, ∞)
To write the inequality in interval notation and graph the interval, we need to split the inequality into two separate parts:
1. For x <= -2: This means that x can take any value less than or equal to -2. In interval notation, we use a square bracket [] to indicate including the end point. Therefore, the interval notation for x <= -2 is [-∞, -2].
2. For x > 0: This means that x can take any value greater than 0. In interval notation, we use a parenthesis () to indicate excluding the end point. Therefore, the interval notation for x > 0 is (0, ∞).
Since we have two separate intervals, we combine them using the union symbol (∪). Therefore, the final interval notation is (-∞, -2) ∪ (0, ∞).
Graphically, the interval would be represented by a number line where all values less than or equal to -2 and all values greater than 0 are shaded, with open circles at -2 and 0 to indicate that those specific values are not included in the interval. The graph would look like this:
(-∞, -2) |----(0, ∞)----|
-2 0