The following expression has been simplified one step at a time. Match each step with the property used to get to that step. (Note: The column that lists the algebraic expressions is already in the correct order.)

(6x + 3) - 5x  multiplicative identity

In this problem, the algebraic expression **(6x + 3) - 5x** is simplified step by step, and each step involves the application of algebraic properties.

The **multiplicative identity property** states that multiplying any number by 1 does not change its value (i.e., \( a \times 1 = a \)). However, this property does not directly apply to the given expression.

Let's first break down the expression to identify which property the multiplicative identity might apply to. The given expression **(6x + 3) - 5x** involves combining like terms (terms with the variable \(x\)).

1. **Step 1: (6x + 3) - 5x**
   - This is the original expression, and no changes have been made yet.

2. **Step 2: (6x - 5x) + 3**
   - This step applies the **commutative property of addition**, which allows you to rearrange terms.
   
3. **Step 3: x + 3**
   - This step applies the **simplification of like terms**, specifically combining the terms \(6x\) and \(-5x\).

Thus, the **multiplicative identity** does not appear to apply directly to this expression. It would typically be seen when a factor of 1 is involved in multiplication, but no such operation is present in the given steps.

Would you like further clarification or details on this? Here are five related questions that might expand on this topic:

1. What is the multiplicative identity property, and how is it applied in algebraic expressions?
2. How do the commutative and associative properties of addition differ?
3. Can you show examples of when the distributive property would apply to simplify expressions?
4. What is the difference between simplifying and factoring an algebraic expression?
5. How would you apply the additive identity property to an algebraic expression?

**Tip:** Always look for common terms or factors when simplifying algebraic expressions—this often leads to faster solutions.

The following expression has been simplified one step at a time. Match each step with the property used to get to that step. (Note: The column that lists the algebraic expressions is already in the correct order.) (6x + 3) - 5x multiplicative identity.

Explore the step-by-step simplification of the algebraic expression (6x + 3) - 5x. Understand how the commutative property of addition and the simplification of like terms are applied. Ideal for students in Grades 6-8.

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