The given equation is:
[tex]\[ 3(x + 12) + y = 3x + 36 + y \][/tex]
To identify which property this equation illustrates, let's break it down step-by-step:
1. Start with the left-hand side of the equation:
[tex]\[ 3(x + 12) + y \][/tex]
2. Apply the Distributive Property: This property states that [tex]\( a(b + c) = ab + ac \)[/tex].
[tex]\[ 3(x + 12) + y = (3 \cdot x) + (3 \cdot 12) + y \][/tex]
Simplifying inside the parentheses:
[tex]\[ = 3x + 36 + y \][/tex]
3. Compare the transformed expression with the right-hand side of the original equation:
[tex]\[ 3(x + 12) + y = 3x + 36 + y \][/tex]
By applying the distributive property, we see:
[tex]\[ 3(x + 12) + y \text{ becomes } 3x + 36 + y \][/tex]
This matches the right-hand side of the given equation exactly, demonstrating that the property used to transform the left-hand side into the right-hand side is the Distributive Property.
### Conclusion
The property illustrated by the equation:
[tex]\[ 3(x + 12) + y = 3x + 36 + y \][/tex]
is the Distributive Property.
