Mrs. Jones wrote an equation on the board. She asked the students to solve for the variable, w. Marcus solved it on his paper using the following steps. Step 1 Step 2 Step 3 w = 4.34 Part A: Review Marcus' work for solving the equation. State the step in which the error occurred, and describe the error using your mathematics vocabulary. (8 points) Part B: Solve the equation, correcting any errors you may find. Show all the steps in your work. (4 points)



Answer :

Answer is as follows-

Let's analyze Marcus' steps and then correct the error:

Marcus' steps:
Step 1: \( w = 4.34 \)
Step 2: (No additional steps provided, assuming he concluded here)
Step 3: \( w = 4.34 \)

Error analysis:

Marcus' error occurred in Step 2 where he concluded the solution without performing any operations to isolate \( w \). In algebra, solving typically involves isolating the variable of interest by performing operations to both sides of the equation until the variable is alone on one side.

Correct approach:

Given the equation:
\[ w = 4.34 \]

To solve for \( w \), there's actually no error in Marcus' final conclusion (Step 3), because \( w = 4.34 \) is a correct solution to the equation given. However, if we were to assume there was an error in not showing intermediate steps, let's explicitly state the correct solving process:

1. Start with the equation:
\[ w = 4.34 \]

2. There are no further operations needed to isolate \( w \) since it is already isolated. Therefore, \( w = 4.34 \) is indeed the correct and final solution.

So, based on the given information and Marcus' work, the correct solution to the equation \( w = 4.34 \) is \( w = 4.34 \). If we interpret the question as identifying the error in not showing intermediate steps, we could say Marcus didn't show the steps of isolating \( w \) explicitly, but the final answer itself is correct.





Exhilerated to help

Shubham Ghosh
MIT