Question

Marcus solved the equation 4(2x−5)=−8(x+1) by following the steps shown below.
Step 1: 8x−20=−8(x+1)
Step 2: 8x−20=−8x−8
Step 3: 8x=−8x+1
Step 4: 16x=12
Step 5: x=3/4
Select THREE statements that correctly justify a step of Marcus’s work.
A.

Marcus applied the distributive property going from the given equation to Step 1.
Marcus used the distributive property to expand the left side of the equation.
B.

Marcus applied the multiplication property of equality going from Step 1 to Step 2.
Step 2 is justified by the distributive property, not by the multiplication property of equality.
C.

Marcus applied the reflexive property of equality going from Step 2 to Step 3.
Step 3 is justified by the addition property of equality, not the reflexive property.
D.

Marcus applied the addition property of equality going from Step 3 to Step 4.
Marcus used the addition property of equality to add 8x8x8x to both sides of the equation.
E.

Marcus applied the division property of equality going from Step 4 to Step 5.
Marcus used the division property of equality to divide both sides of the equation by 16.

Answer 1

A, D, and E.

- A: Marcus used the distributive property to expand 4(2x−5) to 8x−20.
- D: Marcus used the addition property of equality to add 8x to both sides (Step 3 → Step 4).
- E: Marcus used the division property of equality to divide both sides by 16 (Step 4 → Step 5).