Exercise 53 Page 386

In this exercise, we want to graph the given inequality on a number line and determine whether the graph is a segment, a ray or rays, a point, or a line. First, consider the given inequality. This inequality represents all numbers that are greater than or equal to $5$ or less than or equal to $\text{-}2.$ On a number line, this is graphed with a closed circle at $x=\text{-}2,$ with all numbers to the left shaded, and with a closed circle at $x=5,$ with all numbers to the right shaded.

The left piece of the graph starts at $x=\text{-}2$ and continues to the left indefinitely. The right piece of the graph starts at $x=5$ and continues to the right indefinitely. Because both of these pieces have one clear starting point but no endpoint, this graph represents rays.