Question

Identify the property that justifies each step about the answer and the area below. Line 1: (5+x)x line 2: x(x5+x) line 3: x(x+7). line one to line is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property. Line 2 to line 3 is: associative property of addition associative property of multiplication commutative property of addition. Commutative property of multiplication or disruptive property

Answer 1

That's not wright

Answer 2

Let's break down the expressions and the transitions between them to identify the properties used.

1. From **Line 1: (5 + x)x** to **Line 2: x(5 + x)**:
- The property used here is the **Commutative property of multiplication**, which states that changing the order in which two numbers are multiplied does not change the product. Here, \(x\) is factored out, but the expression can also be interpreted as rearranging the multiplication.

2. From **Line 2: x(5 + x)** to **Line 3: x(x + 7)**:
- The property used here is the **Associative property of addition**, which allows us to regroup terms. In this case, \(5 + x\) can be recognized as \(x + 7\) if we assume \(5\) is redefined contextually (perhaps some miscommunication in numerical constants or different problem setups). The transition could involve recognizing that \(x + 5 = x + 7\), through identifying equivalence in context.

Thus, for clarity:
- **Line 1 to Line 2**: Commutative property of multiplication (to rearrange the multiplication).
- **Line 2 to Line 3**: Associative property of addition (reorganizing the addition of terms).

Make sure to check the specific values and context of your problem, as interpretations may vary based on numerals involved.

Answer 3

I apologize for the confusion. Let's carefully analyze each step and the properties involved.

### Step-by-Step Breakdown

1. **From Line 1: (5 + x)x to Line 2: x(5 + x)**:
- The transition here involves moving \(x\) outside of the parentheses. This is justified by the **Commutative Property of Multiplication**. This property allows us to rearrange the order of multiplication.

2. **From Line 2: x(5 + x) to Line 3: x(x + 7)**:
- The transition from \(5 + x\) to \(x + 7\) is not a straightforward application of standard properties of addition; instead, it might involve recognizing that this is an incorrect interpretation without more context provided or a specific calculation leading to that step. However, it seems that one might expect \(5 + x\) to rearrange as \(x + 5\), but this isn't leading to \(x + 7\). It could potentially be a misstatement or typo unless we assume specific values that haven’t been defined.

### Summary of Corrections:
- **Line 1 to Line 2**: **Commutative Property of Multiplication** (moving \(x\) outside).
- **Line 2 to Line 3**: This step is unclear. If we take it literally, mathematically, you couldn’t just change \(5 + x\) to \(x + 7\) without additional context or definition of what \(5\) is being turned into.

If you have specific values for \(x\) or a context that defines the transition from \(5 + x\) to \(x + 7\), please share that, and I'll be happy to clarify further or correct based on the information!