Question

claytons 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. let w represent the number of pounds that claytons bag can weigh. which inequality models the story? \\(w > 50\\) \\(w \geq 50\\) \\(w < 50\\) \\(w \leq 50\\) 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. 25 30 35 40 45 50 55 60 65 70 75

Explanation:

Part 1: Choosing the Inequality

Step1: Understand the Problem

Clayton's bag must weigh no more than 50 pounds. This means the weight \( w \) can be equal to 50 or less than 50.

Step2: Analyze the Inequalities

• \( w > 50 \): Means weight is greater than 50 (not allowed).
• \( w \geq 50 \): Means weight is greater than or equal to 50 (not allowed).
• \( w < 50 \): Means weight is less than 50 (but it can also be equal to 50, so this is incomplete).
• \( w \leq 50 \): Means weight is less than or equal to 50 (matches the requirement).

Step1: Identify the Endpoint

The inequality is \( w \leq 50 \), so the endpoint is at 50. Since the inequality includes 50 (≤), the endpoint is a closed circle (filled in).

Step2: Determine the Direction of the Ray

We need to show all values less than or equal to 50, so the ray should point to the left (towards lower numbers) from 50.

Answer:

\( w \leq 50 \)

Part 2: Graphing the Inequality