Question

graph {x | x ≤ -1 or x > 4}.
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.

Explanation:

Step 1: Analyze the inequality \(x\leq - 1\)

For \(x\leq - 1\), the endpoint \(x = - 1\) is included (closed - circle). The graph is a ray starting at \(x=-1\) and extending to the left (towards more negative values).

Step 2: Analyze the inequality \(x>4\)

For \(x > 4\), the endpoint \(x = 4\) is not included (open - circle). The graph is a ray starting at \(x = 4\) and extending to the right (towards more positive values).

Answer:

On the number - line:

• At \(x=-1\), place a closed - circle (since \(x=-1\) is included in \(x\leq - 1\)) and draw a ray to the left.
• At \(x = 4\), place an open - circle (since \(x = 4\) is not included in \(x>4\)) and draw a ray to the right.