Clayton's family is going to the Bahamas on vacation next week. The airline has a weight limit for luggage. Clayton needs to make sure his bag weighs no more than 50 pounds.

Question

Let w represent the number of pounds that Clayton's bag can weigh. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To model the situation described in Clayton's family vacation using an inequality, we need to express that the weight of Clayton's bag, \( w \), must be no more than 50 pounds. This can be written as:

\[ w \leq 50 \]

This inequality states that the weight \( w \) can be any value up to and including 50 pounds.

Graphing the Inequality

1. Draw a number line: Start by drawing a horizontal line representing the weights.
2. Identify the key point: Mark the point 50 on the number line.
3. Open or Closed Endpoint: Since the inequality is "less than or equal to", you should draw a closed circle at 50 to indicate that 50 is included in the inequality.
4. Shade the appropriate region: Shade to the left of 50 to represent all values of \( w \) that are less than or equal to 50 pounds.

The graph visually represents all weight options for Clayton's bag that satisfy the condition.

Visual Aid

• Closed Circle at 50 to represent weight \( w \) can be 50 pounds.
• Shaded area going left from 50 indicates all possible weights that are less than 50 pounds.

Since I cannot create visual content, feel free to use graphing tools or sketch it based on these instructions!