Alexis solved this equation:

Question

–
2(4p–11)+7p
=
–
10p–14
–
8p+22+7p
=
–
10p–14
–
p+22
=
–
10p–14
9p+22
=
–
14
9p
=
–
36
p
=
–
4
Which property is not needed to justify any of the steps?

Answer 1

To analyze the steps taken in the solution provided, we identify the mathematical properties used:

1. Distributive Property: This is needed to distribute the -2 into the expression \(2(4p - 11)\).
2. Combining Like Terms: This occurs when combining the \(p\) terms on both sides of the equation.
3. Addition and Subtraction Properties of Equality: Used when moving terms from one side of the equation to the other.
4. Division Property of Equality: Applied when isolating \(p\) by dividing by an integer.

The property that is not needed to justify any of the steps is the Associative Property. While it might seem relevant in rearranging terms, it does not directly apply to justify the steps taken in solving the equation in this case. Hence, the Associative Property is the answer.