Nayeli has a points card for a movie theater.
She receives 40 rewards points just for signing up.
She earns 14.5 points for each visit to the movie theater.
She needs at least 185 points for a free movie ticket.

Use the drop-down menu below to write an inequality representing vv, the number of visits she needs to make in order to get a free movie ticket.

To represent the number of visits \( v \) Nayeli needs to make in order to get a free movie ticket, we can create an inequality based on the points she earns.

She starts with 40 points and earns 14.5 points for each visit. She needs at least 185 points for a free ticket, so the inequality would be:

\[
40 + 14.5v \geq 185
\]

This inequality shows that the total points, which consist of the 40 points she received for signing up plus the points earned from her visits, must be at least 185.

Would you like a step-by-step breakdown of how to solve this inequality?

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**Relative Questions:**
1. How would the inequality change if Nayeli needed 250 points instead of 185?
2. What if Nayeli received 50 points for signing up instead of 40?
3. How many visits does Nayeli need to get exactly 185 points?
4. How would the solution change if Nayeli earned 20 points per visit instead of 14.5?
5. Can you find the total points after 5 visits?

**Tip:** Inequalities are very similar to equations but represent ranges of possible values, not just a single solution.

Nayeli has a points card for a movie theater. She receives 40 rewards points just for signing up. She earns 14.5 points for each visit to the movie theater. She needs at least 185 points for a free movie ticket. Use the drop-down menu below to write an inequality representing v, the number of visits she needs to make in order to get a free movie ticket.

Learn how to solve the inequality 40 + 14.5v ≥ 185 to determine the number of visits Nayeli needs to make to earn a free movie ticket. This problem explores algebraic concepts such as linear equations and inequalities, suitable for students in Grades 6-8.

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