Exercise 51 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. The inequality $x\le 3$ represents all numbers that are less than or equal to $3.$ On a number line, this is graphed with a closed circle at $x=3,$ since $x$ can equal $3.$ Other numbers that satisfy this inequality are less than $3.$ Therefore, we need to mark all the numbers lying on the left of the circle.

Finally, we need to determine whether the obtained graph is a segment, a ray or rays, a point, or a line. This graph starts at $x=3$ and continues on to the left indefinitely. If we marked any point lying to the left to point $3,$ for example $2,$ we could say that the graph consists of an endpoint $3$ and all points that lie on the same side of $3$ as this marked point. Therefore, this graph is a ray.