Exercise 53 Page 10

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. x≥5ORx≤-2 This inequality represents all numbers that are greater than or equal to 5 or less than or equal to -2. On a number line, this is graphed with a closed circle at x = -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=-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.