To determine which property of real numbers is illustrated by the equation [tex]\(-6(4x + 5) = -24x - 30\)[/tex], let's break down the equation step-by-step:
1. Original Equation:
[tex]\[
-6(4x + 5)
\][/tex]
2. Applying the Property:
- Here, [tex]\(-6\)[/tex] is being distributed to both terms inside the parentheses, [tex]\(4x\)[/tex] and [tex]\(5\)[/tex].
- This means:
\begin{align}
-6 \cdot 4x & = -24x \\
-6 \cdot 5 & = -30
\end{align}
3. Result After Distribution:
[tex]\[
-6(4x + 5) = -24x + (-30)
\][/tex]
4. Simplified Equation:
[tex]\[
-6(4x + 5) = -24x - 30
\][/tex]
The equation uses the distributive property of multiplication over addition, as it distributes the multiplication of [tex]\(-6\)[/tex] over the terms inside the parentheses.
Therefore, the correct option that describes the property shown in this equation is:
- distributive property
