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
