To determine which property of real numbers is illustrated by the equation [tex]\(5(x-3) = 5x - 15\)[/tex], let's analyze the equation step by step.
1. Start with the left-hand side of the equation: [tex]\(5(x-3)\)[/tex].
2. Apply the property described by the equation to simplify [tex]\(5(x-3)\)[/tex]. This means distributing the multiplication over the subtraction inside the parentheses.
[tex]\[
5(x-3) = 5 \cdot x - 5 \cdot 3
\][/tex]
3. Simplify the expression on the right side:
[tex]\[
5 \cdot x - 5 \cdot 3 = 5x - 15
\][/tex]
4. Now we have:
[tex]\[
5(x-3) = 5x - 15
\][/tex]
This process of distributing the multiplication over the terms inside the parentheses demonstrates a specific property of real numbers. The property that allows us to rewrite [tex]\(5(x-3)\)[/tex] as [tex]\(5x - 15\)[/tex] is known as the Distributive Property.
Thus, the correct answer is:
Distributive Property
