https://file.aiquickdraw.com/mathbot/file/1726496282020nuvby6dj.jpg

The inequality provided in the image is:

\[ 7x > 2x + 30 \]

To write a word problem based on this inequality, we will structure it such that all seven parts mentioned in the prompt are covered.

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**Word Problem:**

Mia is selling concert tickets. She earns $7 for every ticket she sells at a concert. However, her competitor, James, is selling tickets for a different event, and he earns $2 for every ticket he sells, but he also has an additional bonus of $30 from a previous deal.

How many tickets must Mia sell in order to earn more than James?

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**Breaking Down the Equation:**

1. **Correct variable term for the left side expression:** Mia earns $7 per ticket, so the left side of the inequality is $ 7x $, where $ x $ is the number of tickets Mia sells.
2. **Correct constant term for the left side expression:** There is no constant term for the left side in this case (Mia doesn't have any bonus).
3. **Correct operation between the terms of the left side expression:** There is multiplication between 7 and $ x $, representing $7 per ticket.
4. **Correct inequality symbol:** Mia wants to earn more than James, so the inequality is $ > $.
5. **Correct variable term for the right side expression:** James earns $2 per ticket, so the right side has $ 2x $.
6. **Correct constant term for the right side expression:** James receives an additional bonus of $30, hence the constant term is $ 30 $.
7. **Correct operation between the terms of the right side expression:** Addition is used, $ 2x + 30 $, indicating that James earns $2 per ticket plus a $30 bonus.

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### Would you like to solve this inequality now or need further details?

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### Related Questions:
1. How many tickets does Mia need to sell for her earnings to exceed $100 more than James?
2. What if James's bonus increases to $50? How does this affect the inequality?
3. If Mia's earnings per ticket drop to $6, how does that change the number of tickets she must sell to earn more than James?
4. What happens if both Mia and James earn $3 more per ticket than in the original problem?
5. How would the inequality change if Mia has a fixed bonus of $20?

**Tip:** When writing or solving inequalities, remember that the direction of the inequality symbol matters when interpreting real-life situations.

Write a word problem using the inequality 7x > 2x + 30.

Explore how to solve the inequality 7x > 2x + 30 with a real-life scenario. Learn the core concepts of inequalities and linear equations, suitable for students in Grades 7-8.

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