Question

Statement 2(x + 3) = 10 2x + 6 = 10 (2x + 6) - 6 = (10) - 6 (2x + 6) - 6 = 10 - 6 2x + (6 - 6) = 10 - 6 2x + 0 = 10 - 6 2x + 0 = 4 2x = 4 (2x)/2 = 4/2 1x = 2 x = 2 Reason Given Subtraction property of equality a-ba-b Associative property of addition a - a = 0 (Additive Inverse) Substitution a + 0 = a (Additive Identity) Division property of equality Substitution 1a = a (Multiplicative Identity) 自 + < A student solved the given equation and justified every step except one. What is the missing reason? A Associative property of addition B Commutative property of additionMultiplicative property of equalityMultiplicative property of equality
D Distributive property of multiplication over additionDistributive property of multiplication over addition

Answer 1

Let's break down the steps given in the problem and identify where the missing reason might be.

You have the equation:
\[ 2(x + 3) = 10 \]

1. **Distributing**:
\[ 2x + 6 = 10 \]
(Justification: Distributive property of multiplication over addition)

2. **Subtracting 6 from both sides**:
\[ (2x + 6) - 6 = 10 - 6 \]
(Justification: Subtraction property of equality)

3. **Simplifying both sides**:
\[ 2x + 0 = 4 \]
(Justification: Additive Identity)

4. **Removing the zero**:
\[ 2x = 4 \]
(Justification: Substitution)

5. **Dividing both sides by 2**:
\[ (2x)/2 = 4/2 \]
(Justification: Division property of equality)

6. **Simplifying**:
\[ 1x = 2 \]
(Justification: Division property of equality)

7. **Final result**:
\[ x = 2 \]
(Justification: Substitution)

Now, looking at all of these steps, it appears that the missing justification is **step 1**, where you distribute the 2. Since the initial step of expanding \(2(x + 3)\) is an application of the **Distributive property of multiplication over addition**.

Given the options you provided:
- A. Associative property of addition
- B. Commutative property of addition
- C. Multiplicative property of equality
- D. Distributive property of multiplication over addition

The correct answer is **D. Distributive property of multiplication over addition** as the missing reason.