To determine which property of real numbers is being demonstrated by the equation [tex]\(-6(4x + 5) = -24x - 30\)[/tex], we should examine how the terms on the left side of the equation are manipulated to become the terms on the right side.
The left-hand side of the equation is [tex]\(-6(4x + 5)\)[/tex]. Let's break it down:
1. [tex]\(-6\)[/tex] is multiplied by the entire expression inside the parentheses [tex]\((4x + 5)\)[/tex].
2. Using the distributive property, [tex]\(-6\)[/tex] is distributed to both [tex]\(4x\)[/tex] and [tex]\(5\)[/tex].
Mathematically, applying the distributive property looks like this:
[tex]\[ -6(4x + 5) = -6 \cdot 4x + (-6) \cdot 5 \][/tex]
Now, we perform the multiplications:
[tex]\[ -6 \cdot 4x = -24x \][/tex]
[tex]\[ -6 \cdot 5 = -30 \][/tex]
So, the equation simplifies to:
[tex]\[ -24x - 30 \][/tex]
Thus, the left-hand side [tex]\(-6(4x + 5)\)[/tex] is equivalent to the right-hand side [tex]\(-24x - 30\)[/tex] through the application of the distributive property.
Therefore, the property of real numbers shown in the equation [tex]\(-6(4x + 5) = -24x - 30\)[/tex] is the distributive property.
