Question 31

Paul's work includes a mistake in Step 2.

In Step 2, Paul incorrectly simplifies the expression, leading to an error in subsequent steps. The correct simplification should not yield the equation he presents.

A) Step 1

Step 1 is not provided in the extract, thus we cannot determine if any mistake was made. Since there is no context to evaluate, it cannot be identified as the step containing the error.

B) Step 2

In Step 2, Paul makes an arithmetic error when simplifying the expression x - 10x - 20 = 38. The correct simplification should have resulted in -9x - 20 = 38, which is consistent with the subsequent steps, thus indicating that Step 2 is where the mistake occurs.

C) Step 3

Step 3 follows the incorrect simplification from Step 2 but does not contain a new mistake itself. It correctly manipulates the equation from Step 2. Therefore, it cannot be identified as the step with the error.

D) Step 4

In Step 4, Paul correctly isolates -9x from the previous step. Since this step is based on the incorrect result from Step 2, it does not introduce a new mistake but rather continues from the previous error.

E) Step 5

Step 5 calculates x = -58/9, which follows from earlier steps. Although this value is derived from a mistake made in Step 2, the calculation in Step 5 itself is not erroneous. Thus, it does not represent the step with the initial mistake.

Conclusion

The mistake in Paul's work occurs in Step 2, where he incorrectly simplifies the expression, which affects all subsequent steps. Since Steps 3, 4, and 5 build upon this incorrect foundation without introducing new errors, they cannot be identified as the source of the mistake. Hence, Step 2 is definitively the step that contains the error.