Let's analyze the problem and find the correct inequality that describes the scenario.

Problem Breakdown:

• Initial Points: Kaylee gets 80 points just for signing up.
• Points per Visit: She earns 11.5 points for each visit.
• Total Points Needed: She needs at least 210 points to earn a free movie ticket.

Variables:

• Let $v$ represent the number of visits Kaylee makes to the movie theater.

Mathematical Expression:

The total points after $v$ visits is given by the sum of her initial points and the points she earns from visiting: $\text{Total Points} = 80 + 11.5v$ She needs at least 210 points, so we write the inequality as: $80 + 11.5v \geq 210$

Finding the Correct Answer:

The correct inequality is $80 + 11.5v \geq 210$, which matches the second option in the list of answers in the image.

Would you like a step-by-step solution for solving this inequality? Here are five questions to further explore the topic:

1. How many visits does Kaylee need to make if she has already earned 150 points?
2. If Kaylee earns 15 points per visit instead of 11.5, how would the inequality change?
3. What would happen if the number of points required for a free movie ticket increased to 250?
4. If Kaylee visits the theater 5 times, how many points does she accumulate?
5. Can you create a graph showing how her points increase with the number of visits?

Tip: When solving inequalities, treat them similarly to equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number!