Question

graph the compound inequality.
x > -670 and x ≤ -630
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
a segment, ray, or line to delete it.
-680 -670 -660 -650 -640 -630 -620
submit

Explanation:

Step1: Analyze \( x > -670 \)

For \( x > -670 \), the endpoint at \( -670 \) is open (since \( x \) is greater than, not greater than or equal to), so we draw an open circle at \( -670 \) and a ray pointing to the right (towards larger numbers).

Step2: Analyze \( x \leq -630 \)

For \( x \leq -630 \), the endpoint at \( -630 \) is closed (since \( x \) is less than or equal to), so we draw a closed circle at \( -630 \) and a ray pointing to the left (towards smaller numbers).

Step3: Find the intersection

The compound inequality is the intersection of \( x > -670 \) and \( x \leq -630 \). So we need to represent the segment between \( -670 \) (open circle) and \( -630 \) (closed circle). We plot an open circle at \( -670 \), a closed circle at \( -630 \), and draw a segment connecting these two points (since the solution is all numbers greater than \( -670 \) and less than or equal to \( -630 \)).

Answer:

To graph the compound inequality \( x > -670 \) and \( x \leq -630 \):

1. Plot an open circle at \( -670 \) (because \( x > -670 \), not \( x \geq -670 \)).
2. Plot a closed circle at \( -630 \) (because \( x \leq -630 \)).
3. Draw a segment connecting the open circle at \( -670 \) and the closed circle at \( -630 \) (this segment represents all \( x \) such that \( -670 < x \leq -630 \)).