To determine which property is illustrated by the statement [tex]\( 7(x-5) = 7x - 35 \)[/tex], let's break down the equation step-by-step.
Given:
[tex]\[
7(x-5) = 7x - 35
\][/tex]
We need to identify which property matches this equation. Let’s consider our options:
1. Reflexive Property: This property states that any quantity is equal to itself, [tex]\( a = a \)[/tex]. This does not apply here as the statement involves different expressions on each side of the equation.
2. Symmetric Property: This property states that if [tex]\( a = b \)[/tex], then [tex]\( b = a \)[/tex]. This property is not relevant here as it does not explain the transformation of the expression.
3. Transitive Property: This property states that if [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]. The equation given is a single equation, not a series of equations where transitivity can be applied.
4. Distributive Property: This property states that [tex]\( a(b + c) = ab + ac \)[/tex]. Here, we see that the left-hand side [tex]\( 7(x - 5) \)[/tex] involves distributing the 7 to both [tex]\( x \)[/tex] and [tex]\(-5\)[/tex]:
[tex]\[
7(x - 5) = 7 \cdot x + 7 \cdot (-5) = 7x - 35
\][/tex]
This matches with the provided equation:
[tex]\[
7(x - 5) = 7x - 35
\][/tex]
Hence, the property illustrated by the statement [tex]\( 7(x-5) = 7x - 35 \)[/tex] is the Distributive Property.
So, the correct answer is:
Distributive Property
