Question

Q24 Darnell was asked to use and identify appropriate properties of equality to find the value of d that makes this statement -4d – 8 = 2 + d true. He has written out his steps below. Label those steps with the property used.
-4d + 4d – 8 = 2 + d + 4d (________________)
-8 = 2 + 5d (combine like terms)
-8 – 2 = 2 – 2 + 5d (_________________)
-10 = 5d (combine like terms)
-10/5 = 5d/5 (______________________)
-2 = d

Answer 1

Let's label the steps taken by Darnell with the appropriate properties of equality.

1. **-4d + 4d – 8 = 2 + d + 4d**
(Adding the additive inverse of -4d to both sides: **Addition Property of Equality**)

2. **-8 = 2 + 5d**
(Combine like terms)

3. **-8 – 2 = 2 – 2 + 5d**
(Subtracting 2 from both sides: **Subtraction Property of Equality**)

4. **-10 = 5d**
(Combine like terms)

5. **-10/5 = 5d/5**
(Dividing both sides by 5: **Division Property of Equality**)

So the labeled steps would be:

1. **Addition Property of Equality**
2. (Combine like terms)
3. **Subtraction Property of Equality**
4. (Combine like terms)
5. **Division Property of Equality**