x≤59

Question

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To represent the inequality \( x \leq 59 \) on a number line, you would plot the following:

1. Endpoints:

   • Plot a closed dot at \( 59 \) to indicate that \( 59 \) is included in the solution (since the inequality is less than or equal to).
   • There is no endpoint on the left side because \( x \) can take values all the way to negative infinity.

2. Changing an Endpoint:

   • Since the only endpoint is at \( 59 \) and it is already closed (indicating that \( 59 \) is included), you would not change this to open, as that would misrepresent the inequality.

3. Deleting the Middle:

   • Since the left side extends to negative infinity, we don’t specifically delete any segment, ray, or line on the left. However, if you were to visually represent this section of the number line, you can simply show the line extending leftward from \( 59 \) without marking any endpoint. If you're specifically asked to delete the middle beyond \( 59 \) (on the left), you would just indicate that there are no bounds.

Here's a general representation of how you could go about plotting this:

• Closed dot on \( 59 \): ●
• Ray extending infinitely to the left: ←

Thus, the number line would visually look like this:

<------●==============================>
       59

(Where the closed dot represents the inclusion of \( 59 \), and the arrow at the left indicates that the values extend infinitely leftward).