https://file.aiquickdraw.com/mathbot/file/1726487869478hy5im4pc.jpg

The problem in the image asks for an inequality that models the statement:

**"Three times the difference of \( z \) and 9 is no less than -15."**

Let's break this down step by step:

1. **Difference of \( z \) and 9**: This is represented by \( z - 9 \).
2. **Three times this difference**: Multiply the expression by 3, so we get \( 3(z - 9) \).
3. **"No less than"** means "greater than or equal to". So, \( 3(z - 9) \geq -15 \).

Thus, the inequality is:

\[
3(z - 9) \geq -15
\]

Would you like a detailed explanation of how to solve this inequality?

Here are five related questions:
1. How do you solve the inequality \( 3(z - 9) \geq -15 \)?
2. What happens if the inequality sign is reversed in a similar problem?
3. How do you represent inequalities on a number line?
4. What is the difference between solving equations and inequalities?
5. Can you apply this concept to word problems involving more complex scenarios?

**Tip**: Always pay close attention to phrases like "no less than" or "at least," as they determine the direction of the inequality!

Consider the following mathematical statement: Three times the difference of z and 9 is no less than -15. Write an inequality to model the statement.

Learn how to model the inequality 3(z - 9) ≥ -15 based on the given algebraic statement. This problem focuses on algebraic inequalities and the distributive property. Suitable for students in Grades 7-9.

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