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.

Question

-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