\begin{tabular}{l} One of the steps Neesha used to correctly solve an equation is shown below: \ Line $$ 1: 18+8 x-4=13 $$ \ Line $$ 2: 8 x+18-4=13 $$ \ Which set of statements describes the procedure Neesha used to go from line 1 \ to line 2 and identifies the property that justifies that procedure? \ O Neesha changed the order of the 18 and $$ 8 x $$. \ This procedure is justified by the associative property of addition. \ O Neesha changed the order of the 18 and $$ 8 x $$. \ This procedure is justified by the commutative property of addition. \ O Neesha added -18 to both sides of the equation. \ This procedure is justified by the additive inverse property. \ \hline O Neesha added -18 to both sides of the equation. \ This procedure is justified by the additive inverse property of equality. \end{tabular}

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UpStudy AI · Accepted Answer

The correct procedure Neesha used can be identified by analyzing the transition from **Line 1** to **Line 2**:

- **Line 1:** $$ 18 + 8x - 4 = 13 $$
- **Line 2:** $$ 8x + 18 - 4 = 13 $$

**Explanation:**

1. **Changing the Order:** Neesha rearranged the terms $$ 18 $$ and $$ 8x $$ in the equation. Specifically, she changed $$ 18 + 8x $$ to $$ 8x + 18 $$.

2. **Justifying the Procedure:** This rearrangement is justified by the **commutative property of addition**, which states that the order in which two numbers are added does not change the sum. Mathematically, $$ a + b = b + a $$.

**Incorrect Options:**

- **Associative Property:** This property deals with the grouping of numbers being added or multiplied, not the order. Since Neesha changed the order, not the grouping, the associative property does not apply here.
  
- **Adding -18 to Both Sides:** This step is not reflected in the transition from Line 1 to Line 2. Neesha did not perform this operation in the given step.

**Conclusion:**

**Option 2** accurately describes Neesha's procedure and correctly identifies the commutative property of addition as the justification.

**Answer:**

• Neesha changed the order of the 18 and $$ 8 x $$.
 This procedure is justified by the commutative property of addition.
Neesha rearranged the order of 18 and $$ 8x $$ in the equation, which is justified by the commutative property of addition.

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