Let's analyze the given equation [tex]\(2x = 2x\)[/tex].
The statement [tex]\(2x = 2x\)[/tex] compares the quantity [tex]\(2x\)[/tex] to itself. In mathematics, when an equation or equality states that a value is equal to itself, it demonstrates what is known as the Reflexive Property.
The Reflexive Property of equality states that any mathematical expression is always equal to itself. In symbolic terms, for any value [tex]\(a\)[/tex], it always holds that:
[tex]\[a = a\][/tex]
Considering the provided equation:
[tex]\[2x = 2x\][/tex]
Here, the same expression ([tex]\(2x\)[/tex]) on both sides of the equation clearly illustrates this property.
Thus, the property illustrated by the statement [tex]\(2x = 2x\)[/tex] is the Reflexive Property.
### Other Properties (for Clarification)
- Symmetric Property: This states that if one value equals another, then the second value equals the first. Symbolically, if [tex]\(a = b\)[/tex], then [tex]\(b = a\)[/tex]. However, this property is not relevant to the given statement since it does not show equality between two different values.
- Transitive Property: This states if one value equals a second value and the second value equals a third value, then the first value equals the third. Symbolically, if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. This is also not relevant to the given statement as it does not involve three values.
- Distributive Property: This property involves the distribution of multiplication over addition. It is formulated as [tex]\(a(b + c) = ab + ac\)[/tex]. Again, this property is not illustrated by the given statement.
Based on this detailed explanation, the property illustrated in the statement [tex]\(2x = 2x\)[/tex] is the:
[tex]\[
\boxed{\text{Reflexive Property}}
\][/tex]
