The image shows a math problem from an IXL lesson related to simplifying expressions and identifying the missing property. Let's break down and explain the problem step by step.

Problem Breakdown:

1. Expression Given:
   $4z - 9$
   The goal is to simplify and apply the correct mathematical property.

2. Intermediate Step:
   The equivalent expression shown is $9 - 4z$, and the chosen property is Commutative Property of Multiplication.
   However, this appears to be an incorrect selection, because:

   • The commutative property of addition states that the order of addition does not matter, i.e., $a + b = b + a$.
   • The commutative property of multiplication applies only when rearranging the factors in multiplication, e.g., $ab = ba$.
     Here, subtraction is involved, so the commutative property does not apply.

3. Second Simplified Expression:
   $= 36z$
   This is marked as a multiplication step.

Explanation of Properties:

• Commutative Property of Addition: $a + b = b + a$.
• Commutative Property of Multiplication: $ab = ba$.
• Associative Property of Addition: $(a + b) + c = a + (b + c)$.
• Associative Property of Multiplication: $(ab)c = a(bc)$.

Corrections to the Problem:

1. Ensure that the correct property is selected.
   For subtraction or multiplication, verify whether the property aligns with the operation.

2. Multiplication steps should explicitly show the constant being multiplied with the variable (e.g., $4z \cdot 9$).

Would you like a detailed solution for each step, or clarification on specific properties? Let me know!

Here are 5 related questions to extend understanding:

1. What is the difference between commutative and associative properties?
2. Can subtraction use the commutative property? Why or why not?
3. How do you simplify expressions involving multiple variables?
4. What is the distributive property, and when is it applied?
5. How do parentheses change the order of operations?

Tip: Always match the mathematical property with the operation being performed!