ValkyrieRidn
Answered

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Which property is illustrated by this statement?
[tex]\[ 3(x + 12) + y = 3x + 36 + y \][/tex]

A. Reflexive Property: [tex]\( a = a \)[/tex]

B. Symmetric Property: If [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]

C. Transitive Property: If [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]

D. Distributive Property: [tex]\( a(b + c) = ab + ac \)[/tex]

Sagot :

GinnyAnsweridn
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.
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