Olivia is trying to simplify the expression 2+(x+5)

Question

using properties of algebra. She has explained her reasoning in steps, but where did she go wrong?

I can use the Distributive Property to rewrite this expression as (2+x)+(2+5)

Then, I can use the Commutative Property to rewrite it again as (2+5)+(2+x)

I can also use the Associative Property to write the expression as (2+5+2)+x

Finally, I can simplify to show that the expression is equivalent to 9+x
(1 point)
Responses

Step 1
Step 1

Step 2
Step 2

Step 3
Step 3

Step 4

Answer 1

Olivia made an error in her application of the properties of algebra at the very first step. Here’s where she went wrong:

Step 1:

Incorrect Application of the Distributive Property:
Olivia states that she is using the Distributive Property to rewrite the expression \( 2 + (x + 5) \) as \( (2 + x) + (2 + 5) \). This is incorrect. The Distributive Property states that \( a(b + c) = ab + ac \). However, in this case, \( 2 + (x + 5) \) does not involve a term outside the parentheses that can be distributed over them.

Correcting Step 1:

Instead of using the Distributive Property, she should simply evaluate \( (x + 5) \) as is, and recognize that adding 2 does not require any distribution. The correct expression would just be simplified as \( 2 + x + 5 \).

Further Steps:

For the subsequent steps:

• In Step 2, the Commutative Property (which states that the order of addition does not matter) could be applied correctly if Step 1 were correct.
• In Step 3, applying the Associative Property would also make sense if the previous steps were valid.
• In Step 4, simplifying \( 2 + 5 \) to \( 7 \) is valid, leading to \( 7 + x \), rather than \( 9 + x \).

Overall, the error occurred at Step 1 with the improper application of the Distributive Property.