Carter solved the equation, 7(n−4)=28, for n. When he submitted his work, his teacher said that one of his justifications was incorrect. In which step is Carter's justification incorrect?

Step Justification
1. 7(n−4)=28
Given
2. 7n−28=28
Distributive Property
3. 7n=56
Addition Property of Equality
4. n=8
Multiplication Property of Equality

His justification for step 4 is incorrect. It should be "Division Property of Equality"

This is because you divide both sides by 7 to isolate n. This is to undo the multiplication of 7 on the variable n.

On the left side, 7n/7 turns into n. On the right side 56/7 turns into 8.

If you multiply both sides by 1/7, then this would be a valid use of the multiplication property of equality, meaning that Carter would have the correct justification here. However, it seems like your teacher isn't going this route since it seems like they want one of the steps to have a mistake in them. Steps 1, 2, and 3 have correct justifications.

b

step-by-step explanation:

given

- 2 (3x + 12y - 5 - 17x - 16y + 4 )

simplify the parenthesis by collecting like terms

= - 2 (- 14x - 4y - 1) ← distribute the parenthesis by - 2

= 28x + 8y + 2 → b