Question

graph {x | x ≤ -1 or x > 1}. 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:

Step1: Analyze inequality $x\leq - 1$

For $x\leq - 1$, since it includes $x=-1$, we use a closed - circle at $x = - 1$ and shade to the left.

Step2: Analyze inequality $x>1$

For $x>1$, since it does not include $x = 1$, we use an open - circle at $x = 1$ and shade to the right.

Answer:

On the number - line, place a closed circle at $x = - 1$ and shade the line to the left of $x=-1$. Place an open circle at $x = 1$ and shade the line to the right of $x = 1$.