Answered

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Select the correct answer.

Molly rewrote the equation as shown:

[tex]\[
\begin{array}{c}
-5d + 11 = 8 - 3d \\
-5d + 11 + 3d = 8 - 3d + 3d
\end{array}
\][/tex]

Which property did she use to rewrite the equation?

A. Addition property of equality
B. Distributive property
C. Multiplication property of equality
D. Substitution property

Sagot :

GinnyAnswer
Let's examine how Molly rewrote the given equation step by step and identify the mathematical property she used.

### Original Equation
[tex]\[ -5d + 11 = 8 - 3d \][/tex]

### Step 1: Adding [tex]\(3d\)[/tex] to Both Sides
To isolate the variable [tex]\(d\)[/tex], Molly added [tex]\(3d\)[/tex] to both sides of the equation:

[tex]\[ -5d + 11 + 3d = 8 - 3d + 3d \][/tex]

### Simplified Equation
After simplifying both sides:

[tex]\[ (-5d + 3d) + 11 = 8 + ( -3d + 3d ) \][/tex]
[tex]\[ -2d + 11 = 8 \][/tex]

By adding the same expression on both sides of the equation, Molly maintained the equality.

### Conclusion
The property that allows the addition of the same term to both sides of an equation to maintain their equality is known as the addition property of equality.

Thus, Molly used the addition property of equality.

### Answer
The correct answer is:

[tex]\[ \boxed{\text{addition property of equality}} \][/tex]
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