To determine which property Molly used in rewriting the given equation, let's analyze her steps.
Given the original equation:
[tex]\[
-5d + 11 = 8 - 3d
\][/tex]
Molly rewrote it as:
[tex]\[
-5d + 11 + 3d = 8 - 3d + 3d
\][/tex]
Let's break this down step-by-step:
1. Molly started with the original equation:
[tex]\[
-5d + 11 = 8 - 3d
\][/tex]
2. She added [tex]\(3d\)[/tex] to both sides of the equation. This results in:
[tex]\[
-5d + 3d + 11 = 8 - 3d + 3d
\][/tex]
The [tex]\(3d\)[/tex] terms on the right-hand side cancel each other out, simplifying to:
[tex]\[
-5d + 3d + 11 = 8
\][/tex]
Adding the same value to both sides of an equation is known as the addition property of equality. This property ensures that the equality remains true when the same quantity is added to both sides of the equation.
Therefore, Molly used the addition property of equality to rewrite the equation.
So, the correct answer is:
addition property of equality.
