The problem you've uploaded describes Alonso's points card system for earning a free movie ticket. The key points are:

• Alonso gets 40 points just for signing up.
• He earns 12.5 points for each visit to the movie theater.
• He needs at least 185 points to get a free movie ticket.

The inequality given is:

$40 + 12.5x \geq 185$

Where $x$ represents the number of visits Alonso needs to make to earn the free ticket. Let's solve this step-by-step:

Step 1: Subtract 40 from both sides

$12.5x \geq 185 - 40$ $12.5x \geq 145$

Step 2: Divide both sides by 12.5

$x \geq \frac{145}{12.5}$ $x \geq 11.6$

Since Alonso can't make a fraction of a visit, we round this up to the next whole number, which gives:

$x \geq 12$

So, Alonso needs to visit the movie theater at least 12 times to earn his first free movie ticket.

Would you like more details on this? Let me know if you have questions!

5 Related Questions:

1. What happens if Alonso earns 15 points per visit instead of 12.5? How would the inequality change?
2. How many points would Alonso have after exactly 10 visits?
3. What would the inequality look like if Alonso started with 50 points?
4. How could we write an inequality if the free ticket required 200 points instead of 185?
5. What if Alonso wanted to earn two free tickets? How would the inequality adjust?

Tip:

When working with inequalities, always make sure to adjust for real-world situations, like rounding up when the number of visits must be a whole number!