Fill in the blanks and state the property used.
`23+"_______"="________"+23=0`

Options

A. (-23)=(-23)
Property used : commutative property of addition
B. (-23)=(0)
Property used : Additive inverse
C. (0)=(0)
Property used : Additive inverse
D. (-23)=(-23)
Property used : Additive inverse

Answer

To solve the equation \( 23 + "_______" = "________" + 23 = 0 \), we need to find the values that will make both sides equal to zero.

### Step-by-Step Solution:

1. **Understanding the equation**:
We have two parts to fill in. The equation states that when we add something to 23, the result should be zero. This means we need to find a number that, when added to 23, gives us 0.

2. **Finding the first blank**:
To find the first blank, we can set up the equation:
\[ 23 + x = 0 \]
To isolate \( x \), we subtract 23 from both sides:
\[ x = -23 \]
So, we fill in the first blank with \(-23\).

3. **Finding the second blank**:
Now, we need to fill in the second blank in the expression \( y + 23 = 0 \). We can set up a similar equation:
\[ y + 23 = 0 \]
Again, we isolate \( y \) by subtracting 23 from both sides:
\[ y = -23 \]
So, we fill in the second blank with \(-23\).

4. **Final filled equation**:
Now we can write the completed equation:
\[ 23 + (-23) = (-23) + 23 = 0 \]

5. **Stating the property used**:
The property used in this equation is the **Additive Inverse Property**. This property states that for any integer \( a \), there exists an integer \(-a\) such that:
\[ a + (-a) = 0 \]

### Final Answer:
The filled equation is:
\[ 23 + (-23) = (-23) + 23 = 0 \]
The property used is the **Additive Inverse Property**.