Statement Reason

Question

2(x+3) = 10 given
2x+6=10 which property?
(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
Answers:
Associative property of additionAssociative property of addition
B Commutative property of additionCommutative property of addition
C Multiplicative property of equalityMultiplicative property of equality
D Distributive property of multiplication over additio

Answer 1

Let's analyze the steps in the proof based on the statement and the reasons provided:

1. Statement: \( 2(x + 3) = 10 \)
   Reason: Given

2. Statement: \( 2x + 6 = 10 \)
   Reason: Distributive property of multiplication over addition
   This step applies the distributive property, which states that \( a(b + c) = ab + ac \).

3. Statement: \( (2x + 6) + -6 = 10 + -6 \)
   Reason: Addition property of equality
   You can add the same value (in this case, -6) to both sides of an equation.

4. Statement: \( 2x + (6 + -6) = 10 + -6 \)
   Reason: Associative property of addition
   This states that the way you group the numbers when adding does not change the sum.

5. Statement: \( 2x + 0 = 10 + -6 \)
   Reason: From the previous step, since \( 6 + (-6) = 0 \), we simplify accordingly.

6. Statement: \( 2x + 0 = 4 \)
   Reason: Direct calculation, since \( 10 + (-6) = 4 \).

7. Statement: \( 2x = 4 \)
   Reason: Subtracting 0 does not change the value.

8. Statement: \( \frac{2x}{2} = \frac{4}{2} \)
   Reason: Multiplicative property of equality
   This states that if two expressions are equal, you can divide both by the same nonzero number without changing the equality.

9. Statement: \( 1x = 2 \)
   Reason: Simplifying \( \frac{2x}{2} \) gives \( x \).

10. Statement: \( x = 2 \)
    Reason: Direct statement of final solution.

Summary of Answers Corresponding to Reasons:

• \( 2(x + 3) = 10 \): Given
• \( 2x + 6 = 10 \): D (Distributive property of multiplication over addition)
• \( (2x + 6) + -6 = 10 + -6 \): C (Multiplicative property of equality)
• \( (2x + (6 + -6)) = 10 + -6 \): A (Associative property of addition)
• \( 2x + 0 = 10 + -6 \): Logic
• \( 2x + 0 = 4 \): Calculation
• \( 2x = 4 \): Logic
• \( \frac{2x}{2} = \frac{4}{2} \): C (Multiplicative property of equality)
• \( 1x = 2 \): Simplification
• \( x = 2 \): Result

So the correct answer for each step can be summarized as:

1. Given
2. D
3. C
4. A
5. (not needed, but logical step)
6. Calculation
7. (not needed, but logical step)
8. C
9. (not needed, simplification)
10. Result

Would you like to clarify anything else about this proof?