Question

Kris obtained the equation (n(n−20)=n) and claims that, after dividing each side by (n), she gets the equation (n−20=1), which is solved by (n=21). Is Kris​ correct, or has she overlooked a​ possibility?

Choose the correct answer below. Use the Show Work learning aid to provide related calculations and additional reasoning to support your answer.
A. Kris is correct.
B. Kris is not correct since (n=0) is also a solution.
C. Kris is not correct because (n=21) is not a solution.

Answer 1

Kris is not correct because she overlooked the fact that dividing by (n) is invalid when (n)=0, thus missing a possible solution. Additionally, (n=21) is not a solution to the equation when it's properly factored to (n−1)(n−0)=0.

Step-by-step explanation:

Kris obtained the equation (n(n−20)=n) and after dividing each side by (n), she arrived at the equation (n−20=1), which she claims is solved by (n=21). However, Kris is not entirely correct because she overlooked a critical step in solving the equation. Dividing by (n) is only valid if (n) is not zero; thus, there is also a second solution when (n)=0, as dividing by zero is undefined.

When solving the equation (n(n−20)=n), it should be factored to (n−1)(n−0)=0, which provides the two possible solutions: (n=1) or (n=0). Therefore, Kris not only missed the zero as a solution but also incorrectly concluded that (n=21) is a solution, which it is not according to the factored form.