Question

Complete the following stepped out solution to show that -8 + C + 8 - D is equivalent to C - D. -8 + C + 8 - d - 8 + blank + C - D commutative property of addition. Blank + C - D inverse property of addition. C - d identify property of addition

Answer 1

To show that \(-8 + C + 8 - D\) is equivalent to \(C - D\), we will fill in the blanks and explain each step clearly.

1. Start with the original expression:
\[
-8 + C + 8 - D
\]

2. Rearranging the terms (using the commutative property of addition):
\[
-8 + C + 8 - D = (-8 + 8) + C - D
\]
Here, we can say:
- **Blank:** \(-8 + 8\)
- This demonstrates the **commutative property of addition**, which allows us to rearrange the order of the terms.

3. Now, simplify \(-8 + 8\) (using the inverse property of addition):
\[
-8 + 8 = 0
\]
So now we have:
\[
0 + C - D
\]
Here we note:
- This demonstrates the **inverse property of addition**, stating that adding a number and its inverse (negative) results in zero.

4. The identity property of addition tells us that adding zero does not change the value:
\[
0 + C - D = C - D
\]
Here we note:
- **Identity property of addition**: adding zero does not change the value of \(C\).

Therefore, we have shown that:
\[
-8 + C + 8 - D = C - D
\]

Your completed solution with blanks filled in would look like this:

- \(-8 + C + 8 - D\)
- \(-8 + C + 8 - D = (-8 + 8) + C - D\) (Commutative property of addition)
- \(0 + C - D\)
- \(= C - D\) (Inverse property of addition)
- \(= C - D\) (Identity property of addition)

Thus, the final results confirm that \(-8 + C + 8 - D\) is equivalent to \(C - D\).