Question

graph the compound inequality.
6 < x < 9
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.
number line with 4, 5, 6, 7, 8, 9
submit

Explanation:

Step1: Analyze the inequality

The compound inequality is \(6 < x < 9\), which means \(x\) is greater than 6 and less than 9. So the endpoints are 6 and 9, and both should be open circles (since the inequality is strict, not including the endpoints).

Step2: Plot the endpoints

On the number line provided, the points at 6 and 9 should be open circles. Then, the segment between 6 and 9 (excluding 6 and 9) should be highlighted to represent all the values of \(x\) that satisfy the inequality.

(Note: Since this is a graphing task, the visual steps would involve clicking on the endpoints at 6 and 9 to make them open (if they were closed initially) and then selecting the region between 6 and 9 to show the solution set. However, in terms of the description of the graph: there are open circles at 6 and 9, and a line segment connecting the open circles between 6 and 9 on the number line.)

Answer:

To graph \(6 < x < 9\):

1. At \(x = 6\), place an open circle (because \(x>6\), not \(x\geq6\)).
2. At \(x = 9\), place an open circle (because \(x < 9\), not \(x\leq9\)).
3. Draw a line segment connecting the open circles at 6 and 9 to represent all values of \(x\) between 6 and 9.