Answered

Select the correct answer.

Hattie rewrote the equation as shown:
[tex]\[
\begin{array}{l}
9n + 7 - 2n = 4(-n + 5) - 3n \\
9n + 7 - 2n = -4n + 20 - 3n
\end{array}
\][/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



Answer :

GinnyAnswer
To solve the given problem, let's carefully examine the steps Hattie took to rewrite the equation [tex]\[ 9n + 7 - 2n = 4(-n + 5) - 3n \][/tex].

Hattie started with the equation:
[tex]\[ 9n + 7 - 2n \][/tex]
on the left-hand side and
[tex]\[ 4(-n + 5) - 3n \][/tex]
on the right-hand side.

Now, let's focus on the right-hand side of the equation. Hattie applied the distributive property to the term [tex]\( 4(-n + 5) \)[/tex]. The distributive property states that:
[tex]\[ a(b + c) = ab + ac \][/tex]

Applying this property to [tex]\( 4(-n + 5) \)[/tex]:
[tex]\[ 4(-n + 5) = 4 \times (-n) + 4 \times 5 \][/tex]
[tex]\[ = -4n + 20 \][/tex]

So, rewriting the equation, we get:
[tex]\[ 9n + 7 - 2n = -4n + 20 - 3n \][/tex]

By using the distributive property, Hattie successfully transformed the equation. Therefore, the correct answer is:
B. distributive property

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