Question

What is the correct reason for statement 5?

Prove: 5y + 4 + 6(1 + y) = 11y + 10
Statements Reasons

5y + 4 + 6(1 + y) 1. Given
5y + 4 + (6 + 6y)2. Distributive Property
5y + (4 + 6) + 6y3. Associative Property
5y + 10 + 6y 4. Addition
5y + 6y + 10 5. ?
11y + 10 6. Addition
(a) Multiplication
(b) Associative Property
(c) Addition
(d) Commutative Property

Answer 1

The correct reason for statement 5 in the mathematical proof is the Commutative Property of Addition, which allows the rearrangement of terms when they are being added.

Step-by-step explanation:

The question asks to identify the correct reason for statement 5 in the given Proof. The statement transitions from 5y + 10 + 6y to 5y + 6y + 10. The correct reasoning for this change is the Commutative Property of Addition, which states that A+B=B+A. This property is true for the addition of ordinary numbers, such as 2 + 3 giving the same result as 3 + 2. In the context of variable terms in algebra, this property allows us to change the order in which we add terms together without affecting the sum.